AP Physics 1: Algebra-Based FRQ Room

Acceleration from a Velocity-Time Graph

A velocity vs. time graph is provided for an object moving along a straight line, represented by the

Analysis of Angled Motion

A projectile is launched with horizontal and vertical velocity components of $$15$$ m/s and $$20$$ m

Analyzing Changing Vectors: Two-Dimensional Motion

A drone takes off and follows a multi-leg flight path in a horizontal plane. The flight path consist

Analyzing Experimental Data with Error Bars: Acceleration Experiment

An experiment was conducted to determine the acceleration of an object, and the following data with

Analyzing Motion Through Graphical Data

Researchers recorded the motion of a roller coaster, resulting in a complex position vs. time graph

Analyzing Non-Uniform Acceleration from a Velocity-Time Graph

This question challenges you to analyze a velocity-time graph with non-uniform acceleration. Refer t

Analyzing Position vs. Time Graphs

A researcher collected position data over time for a moving object. The resulting graph is provided.

Boat Navigation with Current

A boat aims to travel directly north across a river that is 200 m wide. The river flows east at 3 m/

Car Acceleration and Deceleration Analysis

A car accelerates uniformly from rest with an acceleration of $$3\ m/s^2$$ for 5 s, then travels at

Car Braking Experiment: Uniform Deceleration Analysis

A physics lab performed an experiment on a car braking to a stop. The data collected is summarized i

Determining the Acceleration Due to Gravity Using a Free-Fall Apparatus

In this experiment, students drop a ball from a known height and measure the fall time to calculate

Distance and Displacement Analysis in a Motion Experiment

In a motion experiment, an object moves following a path represented by the provided position vs tim

Effects of Friction on Motion

A block is sliding on a horizontal surface with an initial speed of 12 m/s. Due to friction, the blo

Energy Considerations in Projectile Motion

In a projectile motion experiment, energy conservation principles are used to predict the maximum he

Evaluating Experimental Data on Uniform Acceleration Using the BIG FIVE Equations

An experiment is conducted to study uniformly accelerated motion. Data for time, velocity, and displ

Experimental Determination of Acceleration

In an experiment, a cart's velocity is measured over time and a velocity vs. time graph is plotted.

Field Trip Navigation Vector Analysis

During a school field trip, students travel between three stops along a curvy route. The actual path

Free Fall and Acceleration due to Gravity Lab

Design an experiment to measure the acceleration due to gravity (g) using the free-fall motion of an

Free Fall Experiment Analysis

In a free fall experiment, a small mass is dropped from a certain height and its fall time is record

Free Fall Investigation: Data Consistency with Theoretical Model

A student performs a free-fall experiment and records the following data: | Height (m) | Fall Time

Free Fall Motion Experiment

In this experiment, students drop a ball from a known height and use a stopwatch to measure the time

Free Fall Motion Lab

In a free fall experiment, a ball is dropped from rest. Use the data provided to analyze the motion.

Free-Body Diagram and Kinematics Analysis

A 3-kg block is subject to multiple forces.

Free-Fall vs. Projectile Motion: Impact of Launch Angle

Two objects are launched from the same height with identical initial speeds of 20 m/s but at differe

Interpreting a Velocity vs. Time Graph

Analyze the velocity vs. time graph provided in the stimulus to determine key aspects of the object'

Interpreting Motion Graphs: Position, Velocity, and Acceleration

Examine the provided position vs time and velocity vs time graphs for an object in motion. Answer th

Interpreting Negative Acceleration and Direction Change

An object's velocity is recorded over time, and the data indicate that the velocity changes sign dur

Investigating Initial Velocity in Uniform Acceleration

Design an experiment to investigate how different initial velocities affect the displacement of an o

Kinematics of Circular Motion

A car is traveling around a circular track of radius 50 m at a constant speed of 20 m/s.

Long Jump: Applying Displacement Concepts

An athlete runs 100 m along a curved track and then performs a long jump. The jump is measured to ha

Methods for Calculating Displacement

Design a controlled experiment to compare two different methods for calculating displacement: one us

Motion on an Incline: Kinematics and Friction

A ball rolls down an inclined plane and its position is recorded over time. Answer the following par

Motion Under Gravity: Effects of Air Resistance

This question explores the differences between ideal free fall and motion under the influence of air

Multi-Directional Displacement Analysis

Analyze the following multi-segment path and calculate the displacement and distance.

Net Displacement in Multi-Segment Motion

An object moves along three straight-line segments with different directions.

One-Dimensional Motion with Changing Directions

This question addresses one-dimensional motion where the object changes direction during its movemen

Pendulum Length and Period Experiment

In a pendulum experiment designed to investigate the relationship between length and period, student

Position vs. Time Graph Analysis

A position versus time graph for an object in motion is provided. Answer the following questions bas

Projectile Motion Launch Error

A student sets up a projectile launcher to study the range of a ball. The launcher is fixed at a spe

Projectile Motion with Varying Launch Speeds

A researcher investigates how changes in the launch speed $$v_0$$ affect the range of a projectile l

Projectile Motion: Maximum Height and Range

This question investigates projectile motion. Using the provided initial conditions, answer the foll

Projectile Motion: Maximum Height and Range Calculation

A ball is launched with an initial speed of $$20 m/s$$ at an angle of $$30^{\circ}$$ above the horiz

Projectile Range Optimization

In an experiment, a projectile is launched with the same initial speed at different angles. The rang

Railgun Motion Analysis: Evaluating Claims About High-Speed Acceleration

A research group claims that their railgun experiment achieved a uniform acceleration of $$1000\ m/s

River Crossing Challenge

A boat aims to cross a river that is 100 m wide by pointing directly across. However, the river has

Runner's Route Analysis: Distance vs. Displacement

A runner follows a specific route as shown in the provided diagram. Starting at point A, the runner

Solving Kinematic Equations with Given Data

This question involves using kinematic equations to analyze motion given experimental data. Refer to

Speed versus Velocity

Examine and compare the concepts of average speed and average velocity.

Speed vs. Velocity Analysis from Motion Data

An object moves along a curving path with a varying speed. Answer the following parts:

Speed vs. Velocity Concepts

This question explores the conceptual differences between speed and velocity. Answer the following p

Two-Stage Motion Analysis: Acceleration and Deceleration

An object undergoes two stages of motion. In the first stage, it accelerates uniformly from rest to

Uniform Acceleration Analysis using the BIG FIVE Equations

A car accelerates uniformly from rest for a period of 10 seconds. This experiment uses the BIG FIVE

Uniform Acceleration Data Analysis using Tables

A student records the following data for a toy car undergoing uniform acceleration: | Time (s) | Ve

Uniform and Non-Uniform Acceleration: Evaluating a Claim

A claim has been made that the BIG FIVE equations of motion can be applied even when an object exhib

Uniformly Accelerated Motion in a Car

A car accelerates uniformly from a complete stop with an acceleration of $$2 \; m/s^2$$. Answer the

Uniformly Accelerated Motion: Big Five Equations

A car starting from rest (initial velocity $$u = 0$$) accelerates uniformly at $$3\ m/s^2$$ for 8 s.

Using Graphical Data to Determine Acceleration

A set of experimental data is provided in the table below showing the velocity of an object over tim

Video Analysis of Accelerated Motion

In this experiment, students record a toy car moving along a track using a video camera to determine

Work Done and Energy Considerations in Accelerated Motion

A block on a frictionless surface accelerates uniformly under a constant net force. Consider the blo

Analyzing Equilibrium on an Inclined Plane

An object remains at rest on an inclined plane due to a balance of forces. A researcher explores the

Analyzing Frictional Forces on a Horizontal Surface

A student investigates how friction affects the acceleration of a cart on a horizontal surface by ap

Applied Force at an Angle on a Block

A 10 kg block rests on a horizontal surface with a kinetic friction coefficient of $$\mu_k = 0.3$$.

Centripetal Force Measurement Using a Rotating Bucket

In this experiment, students fill a bucket with water and swing it in a circular path to measure the

Characterizing Friction on a Sloped Surface

An experiment measured the acceleration of blocks sliding down inclined planes with different coeffi

Critical Analysis of an Experiment on Air Resistance in Free Fall

A study reports that when air resistance is taken into account, the acceleration of objects in free

Deceleration in a Braking Car Experiment

A student investigates the deceleration of a car during braking. The velocity vs. time graph below s

Dynamic Analysis of an Incline with Multiple Forces

A researcher examines the motion of a block on an inclined plane that is subject to gravity, frictio

Dynamic Response of a Spring-Connected Mass System

A mass $$m$$ is attached to a spring with a spring constant $$k$$ and is displaced by a distance $$x

Dynamics and Energy Analysis in a Roller Coaster

A roller coaster car of mass 500 kg descends a frictionless track from a height of 20 m.

Dynamics FRQ #14: Rotational Equilibrium on a See-Saw

A uniform see-saw 4.0 m long and weighing 20 kg is pivoted at its center. Child A, weighing 30 kg, s

Dynamics FRQ #16: Terminal Velocity with Air Resistance

A skydiver of mass 70 kg experiences an air resistance force proportional to velocity given by $$F_{

Dynamics FRQ #18: Normal Force on a Curved Surface

A roller coaster car of mass 500 kg travels over the top of a convex hill with a radius of curvature

Dynamics in a Non-Inertial Reference Frame

Consider a 70 kg person inside an elevator that is accelerating upward with an acceleration $$a_e$$.

Dynamics of a Blasting Car Propelled by Explosive Force

A car on a frictionless track is propelled by a controlled explosion that delivers an impulse over a

Dynamics of a Ladder Against a Wall

A ladder of length $$L = 4 * m$$ leans against a frictionless wall and rests on a rough ground with

Dynamics of a Multi-Block Pulley System

Two blocks with masses $$m_1 = 4\ \text{kg}$$ and $$m_2 = 6\ \text{kg}$$ are connected by a rope ove

Dynamics of a Pendulum

Examine the forces acting on a pendulum bob during its swing.

Dynamics Problem 6: Circular Motion and Friction

A car is negotiating a flat circular curve of radius $$r = 20\ m$$. The coefficient of static fricti

Dynamics Problem 7: Action-Reaction in Skater Push-Off

Two ice skaters, Skater A (mass = $$50\ kg$$) and Skater B (mass = $$70\ kg$$), stand at rest on a f

Dynamics Problem 10: Mass Variation in a Rocket

In a model rocket experiment, the rocket's mass decreases over time as fuel is burned. At a particul

Dynamics Problem 14: Impulse and Momentum in a Collision

Two objects collide on a frictionless surface. Object 1 (mass = $$3\ kg$$) moving at $$4\ m/s$$ coll

Dynamics Problem 15: Equilibrium and Net Force

A horizontal beam is held in static equilibrium by several forces acting on it. The forces include a

Dynamics with Air Resistance Approximation

An object of mass 4 kg is dropped and experiences air resistance acting upward with a constant force

Effect of Friction on Circular Motion

In an experiment on circular motion, the maximum speed of an object moving in a circle is determined

Evaluating Media Claims on Inertial and Gravitational Mass

A popular science news article claims that inertial mass and gravitational mass are significantly di

Force Analysis on a Rotating Platform

A 70 kg person stands on a rotating platform of radius 2 m. The platform rotates with an angular spe

Force of Gravity and Inertial Mass

Analyze the differences between gravitational and inertial mass. Use the gravitational force formula

Free-Body Diagram Analysis for Equilibrium

A student constructs free-body diagrams for an object suspended by two cables at different angles, d

Free-Fall Dynamics Experiment

A student uses a motion sensor to record the motion of a freely falling object. The resulting veloci

FRQ3: Apparant Equal Force Pairs in Collisions

An experiment records the forces during collisions between two objects. Analyze the table of force m

FRQ4: Determining Mass from Acceleration Data

In an experiment, a constant net force of 20 N is applied to different masses, and the resulting acc

Impact of Varying Mass on Acceleration

Two carts move along a frictionless track. One cart has mass $$m$$, and the other has a slightly inc

Inclined Plane Dynamics with Friction

A block of mass $$m = 5 ~kg$$ is placed on a 30° inclined plane. The coefficient of kinetic friction

Investigating Air Resistance in Projectile Motion

A projectile launcher is used to fire objects of different shapes. The time of flight and horizontal

Investigating Frictional Forces on an Inclined Plane

Design an experiment to measure the coefficient of kinetic friction for a block sliding down an incl

Investigating Gravitational vs Inertial Mass

In an experiment, a cart is placed on a low-friction track. A known net force is applied to the cart

Investigating Inertial Mass through Force Application Experiments

A student runs an experiment to measure inertial mass by applying different known forces to an objec

Investigating Motion on an Inclined Plane

A student studies a frictionless object's acceleration on an inclined plane by measuring acceleratio

Investigating Reaction Forces on an Accelerating Elevator

An elevator with a mass of 600 kg accelerates upward at 2 m/s². Investigate the forces acting on the

Investigating Tension in a Two-Mass Pulley System

Design an experiment using a two-mass pulley system (Atwood machine) to measure the tension in the c

Investigating the Equivalence of Gravitational and Inertial Mass

Design an experiment to compare measurements of gravitational mass and inertial mass, thereby testin

Investigation of Normal Force Variation on Curved Surfaces

Students use a dynamics cart to travel along a curved track to examine how the normal force changes

Motion Under Variable Friction Conditions

A student studies the effect of different surface textures on the acceleration of a sliding object.

Multi-Stage Motion Under Changing Forces

A student performs an experiment where an object is subjected to different constant forces in two di

Newton’s Third Law in a Collision Event

A study on collisions between hockey pucks claims that the forces measured during the impact do not

Newton's Third Law in Collisions

A diagram illustrating two carts colliding on a frictionless track is provided (see stimulus). Each

Orbital Dynamics in Celestial Mechanics

In celestial mechanics, gravitational forces govern the motion of satellites and planets.

Spring Scale Measurement of Net Force

Students perform an experiment where they attach a spring scale to a block on a horizontal surface t

Testing Hooke's Law in a Spring-Mass System

A student investigates the relationship between force and displacement in a spring-mass system. The

Analysis of the Impact of Varying Mass on Free Fall Acceleration

In a vacuum, free-fall experiments were performed by dropping objects of different masses from the s

Analyzing Gravity Measuring Apparatus Data

A student builds a gravity measuring apparatus that relies on timing the free fall of a small ball t

Artificial Gravity in a Rotating Space Station

A rotating space station creates artificial gravity through centripetal acceleration. Answer the fol

Centripetal Force in a Ball on a String

A ball of mass $$m$$ is attached to a string and swung in a horizontal circle of radius $$r$$ at a c

Centripetal Force Investigation using a Motion Sensor

A student uses a motion sensor to study a small cart moving along a circular track. The procedure in

Comparing Gravitational and Electric Force Effects

A series of experiments compare the magnitudes of gravitational and electric forces between pairs of

Comparing Observed and Predicted Acceleration in Circular Motion

In an experiment, the observed centripetal acceleration was compared with the theoretical prediction

Conical Pendulum Analysis

A conical pendulum consists of a mass $$m$$ attached to a string of length $$L$$, swinging in a hori

Designing a Centripetal Force Experiment

You are tasked with designing an experiment to measure how centripetal force depends on both the spe

Electric Force in Circular Motion: Error Analysis

A student constructs an experiment where a charged ball is made to move in a circular path under the

Electric vs. Gravitational Forces

Two small spheres each have a mass of $$m_1 = m_2 = 0.01\,kg$$ and carry an equal charge of $$q_1 =

Examining the Effects of Altering Angular Speed on Apparent Weight

In a centrifuge, a sample experiences a change in its apparent weight as the rotational speed increa

Experimental Analysis of Centripetal Acceleration

An experiment is conducted by swinging a cart attached to a string in a circle at a constant speed o

Exploring Uniform Circular Motion with a Pulley System

Design an experiment using a pulley system to generate uniform circular motion and measure the centr

Friction and Circular Motion on a Flat Curve

A car negotiating a circular turn on a flat road relies on static friction to provide the necessary

Gravitational vs Electric Force Experiment: Conceptual Error Analysis

A group of students designs an experiment to compare gravitational and electric forces acting on sma

Integration of Gravitational and Electric Field Effects

In a laboratory setup, a test object is placed in a region where both gravitational and electric fie

Investigating Free Fall using Sensor Data

An object is dropped in a vacuum chamber and its displacement is recorded over time using a high-spe

Investigating the Effect of Mass Variation on Circular Motion

Two objects with different masses travel at the same speed along the same circular path. Analyze the

Pendulum Gravitational Acceleration Measurement

A student sets up an experiment using a simple pendulum to measure the gravitational acceleration, g

Planetary Comparison: Gravitational Force and Acceleration

Gravitational acceleration varies from planet to planet based on mass and radius. Consider Earth and

Predicting Motion Changes: Variation in Radius

An object moves in a circular path at constant speed. Consider the effect of changing the radius on

Rotational Dynamics of a Car on a Circular Track

A student simulates the motion of a car on a circular track to study centripetal force and friction.

Simulating Satellite Re-entry: The Role of Atmospheric Drag

Design a simulation experiment to analyze how atmospheric drag influences a satellite's orbital deca

Spring-Connected Particle in Circular Motion

A particle of mass m is attached to a spring (with spring constant k and natural length \(L_0\)) tha

Tension in a Rotating System: Analysis of Centripetal Force

A student investigates the role of tension in a string as the provider of centripetal force in a rot

Transition from Circular to Projectile Motion

This problem investigates the transition of motion from uniform circular to projectile motion when t

Uniform Circular Motion in a Conical Pendulum

A conical pendulum consists of a mass attached to a string that rotates in a horizontal circle, form

Comparative Power Outputs in Different Systems

Two machines are used for similar tasks. Machine A operates at a constant power output of $$2000\;W$

Conservation of Mechanical Energy in a Roller Coaster

A roller coaster car with a mass of 500 kg is released from rest at the top of a hill of height 20 m

Crane Lifting with Force Angle

A crane lifts a 2000 kg load vertically by 10 m using a cable that makes a 15° angle with the vertic

Determining Maximum Height from Kinetic Energy

A projectile of mass 2 kg is launched vertically upward with an initial speed of 20 m/s. Answer all

Energy Conservation in a Mass-Spring Oscillator

A mass-spring oscillator with a mass of 0.5 kg and a spring constant of 200 N/m is investigated. The

Exploring the Relation Between Power Output and Time in Lifting Tasks

Design an experiment to explore how power output varies during the lifting of weights. Power is defi

Force at an Angle: Lifting a Load

A construction worker lifts a heavy load using a rope that makes an angle of $$30^{\circ}$$ with the

Graphical Analysis of a Pendulum's Mechanical Energy

A pendulum is being analyzed in the laboratory. A graph plotting its kinetic energy (KE) and potenti

Interpreting a Free-Body Diagram of a Block on an Incline

Below is a free-body diagram intended to represent a block on an inclined plane. The diagram shows t

Investigating Power Variations in Electric Motor-Driven Lifts

An electric motor is used to power a lift that raises a load at constant speed. The experiment recor

Investigating the Dynamics of Rotational Work and Power in a Flywheel System

A flywheel is accelerated by an electric motor and its angular displacement, applied torque, and tim

Investigating the Effect of Air Resistance on Mechanical Energy in Projectile Motion

Design an experiment to study how air resistance affects the conservation of mechanical energy in pr

Investigating the Relationship Between Force, Displacement, and Power Output Using an Electric Motor

Design an experiment to measure how efficiently an electric motor converts electrical energy into me

Investigation of Power and Efficiency in a Motorized Lifting System

A researcher tests an electric motor used to lift loads. In an experiment, the motor lifts a 30 kg l

Kinetic Energy and Braking Force

A vehicle of mass $$1200 kg$$ is traveling at $$20 m/s$$ and comes to a stop over a distance of $$40

Kinetic Energy Measurement in a Cart Acceleration Experiment

A researcher accelerates a 2 kg cart along a straight, level track. The cart starts from rest and re

Mechanical Energy in a Roller Coaster Experiment

This question involves analyzing experimental data from a roller coaster where changes in height and

Mechanical Energy in a Spring-Loaded Apparatus

A researcher investigates a spring-loaded mechanism. A spring with a spring constant of $$k = 200 \;

Power and Efficiency in an Electric Motor

An electric motor receives 5000 J of input energy over 10 seconds and produces 3500 J of useful mech

Power Calculation for Lifting Equipment

A lifting crane raises a $$1000\;kg$$ load vertically by $$10\;m$$ in $$20\;s$$. Calculate the work

Quantitative Analysis of Frictional Work

Examine the provided data which quantifies work done by friction on surfaces of varying roughness. A

Testing the Work-Energy Theorem with a Sliding Car

Develop an experiment using a small toy car on a track to test the work-energy theorem, which states

Time-Dependent Power Output Analysis

A weightlifter's performance is recorded over an 8-second interval. The following data shows the wor

Variable Force and Work Done Analysis

An experiment measures the work done on an object subjected to a variable force. The force versus di

Work and Efficiency in a Pulley System

A researcher experiments with a pulley system used to lift a mass. A 10 kg mass is lifted vertically

Work Done Against Friction on a Sliding Block

A block slides on a rough horizontal surface and comes to a stop due to friction. The work done by f

Work Done at an Angle

A force of 100 N is applied to a crate at an angle of 40° above the horizontal, moving the crate 5 m

Work Done on an Inclined Plane

A block is pulled up a 25° inclined plane by applying a force F that makes an angle φ with the incli

Work-Energy Calculations in a Laboratory Experiment

In a lab experiment, a cart is subjected to a constant force during three separate trials as it move

2D Momentum Conservation Analysis

In a two-dimensional collision, two objects exhibit the following velocities (in m/s) before and aft

Air Track Momentum Experiment

In an air track experiment, two gliders undergo a collision. Glider 1 (mass $$0.50\,kg$$) has an ini

Automotive Crumple Zone Analysis

Engineers are analyzing the performance of crumple zones in automobiles during collisions. A car of

Collision Analysis on a Low-Friction Track

In a laboratory experiment, two carts (A and B) on a low-friction track undergo a collision. You are

Comparative Collision Dynamics

Two identical balls are thrown toward a rigid wall from the same height at a speed of $$9$$ m/s. One

Comparing Elastic and Inelastic Collisions

Two objects undergo collisions under different conditions. Experiment 1 features an elastic collisio

Design an Experiment to Verify Momentum Conservation

Design a controlled laboratory experiment to verify the law of conservation of linear momentum. Your

Designing a Lab Experiment to Measure Impulse

You are tasked with designing an experiment to measure the impulse delivered to a cart during a coll

Determining the Coefficient of Restitution

A ball of mass $$0.5 \ kg$$ is thrown against a wall with a speed of $$10 \ m/s$$. After rebounding

Explosive Separation: Momentum Analysis

A stationary object with a mass of 50 kg explodes into two pieces. Experimental data shows that Piec

Flawed Timing Measurements in a Cart Collision Experiment

In this experiment, two carts on an air track collide, and photocell timers are used to measure the

Impulse-Momentum Theorem: Graph Analysis

A force-time graph is provided showing the force exerted on an object during a collision. Use the gr

Inelastic Collision: Objects Sticking Together

A 2 kg cart moving at $$8\,\text{m/s}$$ collides with a 3 kg cart moving at $$4\,\text{m/s}$$ in the

Investigating Collision Outcomes on an Air Track

Design an experiment on an air track to study the outcomes of collisions between carts. Answer the f

Investigating Momentum Conservation in a Pendulum Collision

Two pendulum bobs, each of mass $$1.5 \ kg$$, are suspended. Bob A is set in motion and collides wit

Measurement Errors in Momentum Experiments

A lab report on momentum measurements describes various experiments. Answer the following: (a) Iden

Momentum and Collision Analysis on a Frictionless Track

Consider the collision on a frictionless air track where two carts collide. The following table prov

Momentum in Explosions

A projectile of mass 1.2 kg is moving horizontally at 20 m/s when it explodes into two fragments. On

Momentum in Two-Dimensional Collisions

Two objects collide in a two-dimensional setting. Object A (mass = 2 kg) moves east at 6 m/s, and Ob

Momentum Transfer in an Explosion

A stationary object with mass $$12\,kg$$ explodes into two fragments. One fragment, with a mass of $

Rebounding Ball Momentum Change

A ball of mass $$0.5\,kg$$ moving at $$3.0\,m/s$$ strikes a wall perpendicularly and rebounds with t

Role of Friction in Momentum Transfer

Analyze how friction impacts momentum conservation in a system that is not perfectly isolated.

Segmented Collision Momentum Analysis

A collision is recorded using high-speed imaging, yielding discrete measurements of an object's mome

Simulated Momentum Data Analysis

A computer simulation provides data for collisions in a controlled environment. Answer the following

Soccer Player Collision Analysis

During a soccer match, two players collide. Player A (mass 70 kg) is running at 6 m/s and Player B (

Two-Dimensional Collision Analysis

On a nearly frictionless air hockey table, two pucks (mass = 0.2 kg each) collide elastically. Puck

Amplitude and Force in SHM

In a controlled experiment, a mass attached to a spring is observed while varying the amplitude of o

Analysis of the Effects of Gravity on Pendulum SHM

A pendulum’s period is influenced by the gravitational acceleration in its environment.

Analyzing SHM Data from a Pendulum Experiment

A student collected data on the time taken for 10 oscillations for various pendulum lengths. The dat

Calculation Error in Determining Angular Frequency

A student sets up an experiment to measure the angular frequency (ω) of a mass-spring oscillator by

Comparative Study: Mass-Spring System vs. Pendulum

Compare a mass-spring oscillator and a simple pendulum, noting that both systems exhibit simple harm

Conservation of Energy in SHM

An experiment monitored the kinetic and potential energies of a mass-spring system undergoing simple

Damped Oscillations in a Mass-Spring System

A mass-spring oscillator subject to damping is described by the equation $$x = A e^{-b*t}\cos(ω*t)$$

Determining Phase Constant in SHM

A mass-spring oscillator is described by the displacement equation $$x(t) = A \cos(\omega*t + \phi)$

Determining Spring Constant from Oscillation Data

A student measures the period of a spring-mass system for different masses. The following data is co

Effect of Mass on Angular Frequency in SHM

In a series of experiments on a mass-spring oscillator, the angular frequency was measured for diffe

Effect of Mass Variation on Oscillation Period

In an experiment, the period of oscillation for a spring-mass system is measured for different masse

Effect of Phase Angle on SHM Motion

A researcher studies the effect of changing the phase angle $$\phi$$ in the SHM equation $$x = A \co

Effect of Spring Constant on Oscillatory Motion

In a series of experiments, a mass-spring system is tested using springs with different spring const

Energy Transformations in SHM

A block attached to a spring oscillates horizontally on a frictionless surface. The potential energy

Error in Relating Frequency to Energy in SHM

A student investigates the relationship between frequency and total mechanical energy in a mass-spri

Experimental Determination of Angular Frequency

An experiment recorded the displacement of a mass-spring oscillator at various times (see table belo

Exploring Non-Ideal Behaviors in SHM

In an experiment using a mass-spring system, deviations from ideal SHM are observed, including gradu

Force Analysis in SHM

Analyze the force exerted by a spring on a mass undergoing simple harmonic motion using Hooke's law.

Graphical Estimation of SHM Parameters

A researcher obtains a graph of angular displacement versus time for a pendulum. The following graph

Investigating the Impact of Changing Mass on Oscillation Frequency

A researcher increases the mass attached to a spring and records the oscillation period for each cha

Investigating the Role of Mass in SHM

Explore how varying the mass attached to a spring affects the dynamics of SHM, specifically focusing

Non-Ideal Oscillations: Driven Harmonic Motion

A mass-spring oscillator is subjected to an external periodic force, resulting in driven harmonic mo

Non-linear Effects in Large Amplitude Oscillations

For a mass-spring system, the period is independent of amplitude only for small oscillations. At lar

Pendulum Clock Accuracy and Errors

A pendulum clock relies on the period of a simple pendulum to keep time. However, factors such as ai

Pendulum Motion Comparison

Pendulums are a common example of systems exhibiting periodic motion. Answer the following:

Pendulum Period Calculation

A simple pendulum in a clock tower has a length L = 2.5 m. Answer the following: (a) Derive the expr

Restoring Force and Negative Sign

Hooke's Law states that the force exerted by a spring is given by $$F = -k*x$$. For a spring with co

Testing Amplitude Independence of Period in SHM

An experiment is designed to test the hypothesis that the period of an ideal mass-spring system unde

Amusement Park Ride Safety Check

An amusement park ride features a long rotating arm 10 m in length with a seat at the end. The ride

Analysis of Angular Displacement Graph

An experiment measured the angular displacement of a rotating wheel over time. The graph provided (s

Analysis of Rotational Energy Data

An experiment measured the rotational kinetic energy of a rotating object at various angular velocit

Angular Displacement Calculation from Non-Uniform Acceleration

A rotating object has an angular acceleration that varies with time according to the function $$\alp

Calculating Angular Displacement and Angular Velocity

In a lab setup, a car is moving along a circular track. Analyze the following data to determine its

Center of Mass in Rotational Systems

A non-uniform bar of length 2 m has its left half weighing 3 kg and its right half weighing 5 kg. (a

Centripetal and Tangential Acceleration in Circular Motion

A particle moving in a circle of radius $$0.8 \;m$$ has its angular velocity increase uniformly from

Comparing Rotational Inertia: Disk vs. Ring

Two objects—a solid disk and a ring—each with a mass of 1 kg and a radius of 0.5 m, are subjected to

Connecting Linear and Angular Motion on a Rotating Disc

A point on the edge of a rotating disc is observed, and its motion is characterized by both linear a

Conservation of Angular Momentum Experiment

Design an experiment using a rotating stool and movable weights to investigate the conservation of a

Conservation of Angular Momentum Figure Skater Experiment Error

To simulate a figure skater's spin, a student sets up a rotating platform with adjustable masses rep

Designing a Robot Arm: Optimizing for Rotational Motion

A robotics engineer is designing a robot arm and needs to optimize its rotational motion. Analyze th

Energy Conversion in a Flywheel System

A flywheel with a moment of inertia $$I = 0.3 \;kg\cdot m^2$$ rotates at an angular velocity of $$\o

Experimental Analysis of Rotational Deceleration

A rotor is observed to decelerate uniformly, and the following data for angular velocity $$\omega$$

Free-Body Diagram Analysis for Rotational Equilibrium

Analyze the torques acting on a pivoted body using the data provided and determine if the system is

Frictional Torque on a Rotating Platform

A rotating platform initially spins at 4.0 rad/s and comes to a complete stop in 12 seconds due to f

Investigating Rotational Kinetic Energy vs. Linear Kinetic Energy

A researcher is comparing the rotational kinetic energy of a spinning wheel to the linear kinetic en

Investigating the Effect of Changing Radius on Angular Velocity

A rotating system experiences a change in its radius. Use the data provided to analyze the effect of

Rotational Dynamics and Frictional Torque Error

In an experiment on rotational dynamics using a spinning disk, a student applies a constant force to

Rotational Dynamics with Friction

A turntable with a moment of inertia $$I = 0.4 \;kg\cdot m^2$$ is subject to a constant frictional t

Rotational Energy and Dynamics

This question focuses on the energy aspects of rotational motion. You will calculate the rotational

Rotational Motion in Automotive Braking

A researcher studies the effect of a braking torque on a car wheel. The wheel has a radius of $$R =

Rotational Motion in Planetary Systems

A researcher studies the rotational motion of a small asteroid that rotates with an angular velocity

Satellite Attitude Control Using Reaction Wheels

A satellite utilizes reaction wheels for attitude control. One of its reaction wheels has a moment o

Spinning Bicycle Wheel Damping Experiment Error

A student investigates the deceleration of a spinning bicycle wheel by measuring its angular velocit

Torque and Angular Momentum in a Rotating Machine

A rotating machine experiences varying torques over different time intervals. Use the data provided

Torque and Equilibrium on a Seesaw

A researcher is studying the rotational equilibrium of a seesaw. A 4 m long seesaw has its pivot at

Torque-induced Precession in a Gyroscope

This problem examines the phenomenon of gyroscopic precession when an external torque is applied to

Verification of Linear and Angular Velocity Relationship Error

A student verifies the relationship $$v = rω$$ using a rotating wheel. Measurements of linear speed

Work and Energy Transfer in Rotational Motion

Analyze the work done on a rotating system by examining the provided graph of torque versus angular