AP Physics 1: Algebra-Based FRQ Room

Acceleration and Deceleration Phases in Vehicle Motion

A car accelerates uniformly from rest to 40 m/s in 8 s and then decelerates uniformly to 0 m/s in 4

Analyzing Position vs. Time Graphs

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

Angle of Projection Variation in Projectile Motion

In a controlled experiment, projectiles are launched with a fixed initial speed at various angles. T

Angled Motion and Range Calculation

A projectile is launched from a horizontal platform with an initial speed of $$25\ m/s$$ at an angle

Angled Motion: Maximum Height Experiment

Design an experiment to determine how the launch angle affects the maximum height reached by a proje

Angled Projectile Motion Analysis

In a lab, projectiles are launched at various angles with a constant initial speed. The horizontal a

Average Speed vs. Instantaneous Velocity in Commute Analysis

A commuter’s daily travel is recorded on a detailed position vs. time chart which includes periods o

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 Crash Analysis: Motion Under Deceleration

During a crash simulation, a car decelerates uniformly from 25 m/s to 0 m/s in 4 seconds. Analyze th

Car Deceleration: Acceleration and Deceleration Phases

A car undergoes two distinct phases of motion as recorded in the table below.

Car Motion: Scalar vs. Vector Analysis

A car travels in two segments: first 100 m due north, then 50 m due east. Use the provided table to

Comparative Analysis of Speed and Velocity Measurements

A radar system records both the speed and displacement of a vehicle over time. Answer the following

Comparing Scalar and Vector Quantities

An experiment records both the scalar speed and the vector velocity of an object during several tria

Comparing Speed and Velocity in Curved Paths

A runner moves along a curved track, starting and ending at the same point. Explore the relationship

Designing a Motion Experiment: Investigating Distance, Displacement, Speed, and Velocity

You are tasked with designing an experiment using a motion sensor and a track to investigate the rel

Determining Maximum Height in Projectile Motion Experimentally

A student performs a projectile motion experiment and records the vertical displacement of a ball ov

Distance and Displacement in a Hiker's Journey

A hiker embarks on a journey with four segments as given in the table below. Using the information p

Distance and Displacement: Experimental Analysis

In this experiment, you are investigating the difference between distance and displacement using a m

Distance vs. Displacement: Analyzing Motion Paths

A researcher records the motion of a toy car along a winding track. The car moves from point A to B

Effect of Launch Angle on Projectile Motion

A projectile is launched with an initial speed of 25 m/s at two different angles: 30° and 60°. Analy

Evaluating Air Resistance in Projectile Motion

An experiment measured projectile ranges at various launch angles. Compare the theoretical and measu

Evaluating Motion from Position vs Time Graph: Acceleration Analysis

Examine the following position vs time graph represented by the function $$s(t)=5*t - 0.1*t^3$$. Ans

Experiment on Motion with Resistive Forces

A block is observed sliding on a rough horizontal surface where friction (a resistive force) affects

Experimental Exploration of Distance and Displacement

A mini car is programmed to follow a winding track with curves and turns. Design a laboratory experi

Force and Acceleration Vector Analysis

A constant net force is applied to a 2 kg object.

Free Fall and Acceleration: Analyzing Data

An object is dropped from rest, and its displacement is recorded at various time intervals. Using th

Free Fall and Gravitational Acceleration

A researcher conducts a free-fall experiment by dropping a ball from different heights and recording

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 Experiment Analysis

In a free fall experiment, an object is dropped from rest. Its fall is recorded in the table below.

Free Fall from a Building

An object is dropped from rest from the top of a 45 m tall building.

Free Fall Motion: Dropped Object

An object is dropped from a height of $$45 \text{ m}$$. Assume the acceleration due to gravity is $$

Graph Analysis: Position vs. Time

A researcher records the motion of an object and plots its position (m) versus time (s) on the graph

Horizontal Launch from Elevated Platform

A researcher studies a projectile launched horizontally from an elevated platform. The platform is 2

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

Investigating Scalar and Vector Quantities: Speed vs. Velocity

Design a laboratory experiment to measure an object's speed and velocity using motion sensors and ti

Investigating the Effect of Mass on Accelerated Motion on an Incline

Design an experiment to examine how changing the mass of an object affects its acceleration on an in

Investigation of Newton's Second Law: Force, Mass, and Acceleration

A student sets up an experiment on a low-friction track where a cart is attached to a hanging mass v

Kinematics of a Toy Car: Acceleration and Deceleration

Design an experiment to analyze the acceleration and deceleration patterns of a toy car on a track.

Motion on an Inclined Plane

A 2 kg block slides down a smooth, frictionless inclined plane making a 30° angle with the horizonta

Motion on an Inclined Plane

A block slides down a frictionless inclined plane with an acceleration of $$3.5$$ m/s^2. Starting fr

Motion Sensor and Staircase Displacement Experiment

In this experiment, a motion sensor is used to track a subject as they walk up and down a flight of

Multi-Dimensional Projectile Motion Analysis

In this advanced experiment, a projectile is launched in a two-dimensional plane and its motion is r

Multi-phase Problem on Uniformly Accelerated Motion with Multiple Phases

A car undergoes a three-phase journey: it accelerates from rest, cruises at constant speed, and then

Non-Uniform Acceleration Investigation

A velocity vs. time graph for an object is provided where the graph is curved (non-linear). Answer t

Path Analysis: Distance vs. Displacement

An object moves along a path composed of three segments: first, it travels 4 m east, then 3 m north,

Pendulum Experiment to Measure Gravity

A researcher uses a simple pendulum to determine the acceleration due to gravity. Small swing angles

Position vs Time Graph Analysis

A position vs. time graph for an object in one-dimensional motion is provided. Answer the following

Position vs. Time Graph Analysis

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

Position vs. Time Graph Analysis

Examine the following position vs time graph which is composed of two segments: an initial curved se

Projectile Launch Analysis

A projectile is launched with an initial speed of $$20 \text{ m/s}$$ at an angle of $$30^\circ$$ abo

Projectile Motion Analysis

A projectile is launched with an initial speed of $$20 \; m/s$$ at an angle of $$30^\circ$$ above th

Projectile Motion with Air Resistance

Develop an experiment to investigate the effect of air resistance on projectile motion by comparing

Projectile Motion with Air Resistance Approximation

An experiment studies projectile motion under nearly ideal conditions. A projectile is launched with

Projectile Motion: Maximum Height and Range

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

Projectile Range Optimization

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

Real-World Application: Rescue Helicopter Drop

A rescue helicopter flying horizontally at 15 m/s at an altitude of 50 m drops a supply package. Neg

Relative Motion of Two Cyclists

Two cyclists start from the same location but travel in perpendicular directions. Analyze their rela

Resolving Force Components on an Inclined Plane

A 10-kg block rests on a 30° inclined plane. Analyze the gravitational forces by resolving the weigh

Robot Navigation: Multiple Vector Addition

A researcher programs a robot to move in the following sequence: 1. 80 m due east, 2. 60 m at 30° no

Simulated Impact Test: Speed and Velocity

In a crash simulation lab, a test vehicle decelerates from a high speed and various sensors record i

Skateboard Ramp Projectile Motion

A skateboarder launches off a ramp with an initial speed of $$15\ m/s$$ at an angle of $$20^\circ$$

Speed vs. Velocity Concepts

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

Speed vs. Velocity Measurement Design

Propose an experiment to investigate the differences between speed (a scalar quantity) and velocity

Two-Dimensional Displacement Analysis

A delivery drone flies in two legs. First, it flies 8 m due east. Then, it flies 6 m at an angle of

Uniform Acceleration Analysis Using BIG FIVE Equations

A car starting from rest accelerates uniformly. Data for a trial is provided below. Use the provided

Uniform Acceleration and Displacement of a Car

A car starting from rest accelerates uniformly at 5 m/s² for 10 seconds. Analyze this motion using k

Uniform Acceleration with the BIG FIVE Equations

A car accelerates uniformly from rest.

Uniform Acceleration with Variable Initial Velocities

Two vehicles start moving with different initial velocities but share the same constant acceleration

Uniformly Accelerated Motion and BIG FIVE Equations Lab

A lab experiment involves releasing a cart from rest down a ramp to study uniformly accelerated moti

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

Vector Addition in a Multi-Leg Journey

A delivery truck follows a route consisting of three legs: it travels 10 km east, then 5 km north, a

Vector Addition in Displacement Measurement Error

A student conducts an experiment where a robot moves in two distinct straight-line segments with a c

Vector and Scalar Distinctions in Experimental Data

An experiment recorded various physical quantities as shown in the table below. Identify which quant

Acceleration vs. Net Force Graph Analysis

A series of experiments are conducted where various net forces are applied to an object of constant

Action-Reaction Forces in Collisions

Examine and apply Newton’s Third Law in the context of collisions. Explore the concept of equal and

Action-Reaction in Everyday Life

Newton's Third Law states that every action has an equal and opposite reaction. Evaluate this law in

Analysis of an Acceleration vs. Time Graph

A graph of acceleration versus time for an object is provided. Use the graph to analyze the impulse

Analysis of Forces during a Car Crash

A 1200 kg car moving at 20 m/s crashes into a stationary barrier and comes to rest in 0.25 s. Use im

Analyzing Impulse in a Collision

During a collision experiment, the force exerted as a function of time is recorded, and the graph be

Applying Newton's Second Law

Investigate Newton's Second Law through both theoretical derivation and experimental data.

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

Designing a Pulley System to Study Accelerated Motion

Develop an experimental design using an Atwood machine (a pulley system with two masses) to measure

Designing a Safety System Using Dynamics Principles

Engineers are designing a safety harness system for vehicles to minimize forces on passengers during

Dynamic Equilibrium in a Swinging Object

A child on a swing momentarily comes to rest at the highest point of the swing. Analyze the forces a

Dynamic Equilibrium on a Rotating Platform

A person stands on a rotating platform and remains stationary relative to it. The person is located

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 Experiment 1: Inclined Plane Acceleration

A student sets up an inclined plane with an adjustable tilt angle to measure the acceleration of a c

Dynamics Experiment 9: Free Fall Acceleration Measurements

A student performs an experiment to measure the acceleration due to gravity by dropping various obje

Dynamics Experiment 15: Ramp Experiment with Variable Mass

A student performs an experiment in which a cart is accelerated down a ramp while additional weights

Dynamics FRQ #15: Pendulum in a Non-Inertial Frame

Inside an accelerating car (a = 3 m/s²), a pendulum hangs from the roof.

Dynamics in an Amusement Park Ride

Consider an amusement park ride where a car moves along a vertical loop of radius $$r$$. The car has

Dynamics Investigation: Force, Mass, and Acceleration Experiment

Students conduct an experiment using a dynamic cart where they apply different net forces and measur

Dynamics of a Falling Object with Parachute

An 80 kg skydiver is in free fall before deploying her parachute. After deployment, the parachute pr

Dynamics of a Rotating System: Loop-the-Loop Analysis

In a loop-the-loop experiment, a small object of mass 0.5 kg moves through loops of different radii.

Dynamics of Coupled Oscillators: Mass-Spring Systems

A researcher examines a system of two coupled oscillators connected by a spring to study the interpl

Dynamics on an Inclined Plane

A block of mass $$m$$ is placed on a frictional incline with an angle $$\theta$$ relative to the hor

Dynamics Problem 2: Forces on an Inclined Plane

A block of mass $$m = 8\ kg$$ is placed on a frictionless incline that makes an angle $$\theta = 30^

Dynamics Problem 20: Torque and Rotational Equilibrium in a Beam

A uniform beam is pivoted about one end and is subjected to several forces at various distances from

Effect of Variable Mass on Acceleration

A moving cart is subjected to a constant applied force, but additional mass is being added to the ca

Force Analysis on Explosive Separation

Two objects initially connected separate due to an internal explosion. Object A has mass $$m_A = 1 *

FRQ8: Rolling Cylinder Dynamics on an Inclined Plane

A cylinder rolls down a nearly frictionless inclined plane without slipping. The measured accelerati

Gravitational Variation with Distance

An experiment is conducted to study how the gravitational force between two objects varies with dist

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 Experiment: Investigating Frictional Forces

A group of students claims that the coefficient of static friction for a wood block on an inclined p

Investigating Action-Reaction Forces

In an experiment, two carts in contact on a track, equipped with force sensors, record the forces ex

Investigating Force Transmission in Mechanical Systems

A researcher studies a series of connected masses and springs to explore how an applied force is tra

Investigating Inertia and Mass Relationship

A researcher conducts an experiment to study how the inertia of an object (its resistance to acceler

Investigation of Newton's Third Law Using Collision Experiments

Two gliders on an air track undergo a collision, and force sensors measure the force versus time dur

Motion Under Variable Friction Conditions

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

Newton's Third Law in Rebounding Collisions

A ball is dropped from a height and rebounds off a rigid surface.

Normal Force and Friction in Circular Motion

A car navigates a banked curve. Consider the forces acting on the car as it moves along the curved,

Pendulum Experiment for Gravitational Acceleration

A student sets up a pendulum with a long string and heavy bob to measure the gravitational accelerat

Projectile Motion and Dynamics Analysis

An object is launched into projectile motion. Neglect air resistance and assume that gravity is the

Rotational Dynamics on a Pivot

A student investigates rotational dynamics by applying a tangential force at the edge of a rotating

Rotational-Translational Dynamics in a Rolling Cylinder

A student investigates a cylinder rolling down an inclined plane without slipping. The experiment in

Static Friction and Threshold of Motion

A 5 kg block on a horizontal surface is gradually pushed until it starts to move. The minimum force

Static vs. Kinetic Friction Experiment

Investigate the differences between static and kinetic friction through definitions, experimental da

Testing Hooke's Law in a Spring-Mass System

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

Torque and Rotational Equilibrium on a Seesaw

Students set up a seesaw experiment to study the effects of weight distribution on torque. They plac

Two-Block System on Different Surfaces

In this experiment, two blocks connected by a string over a pulley are placed on surfaces with diffe

Verifying Newton's Second Law in a Lab Experiment

In a lab experiment, a cart on a frictionless track is subjected to different applied forces. The ac

Analyzing Orbit Stability using Energy Considerations

A satellite's orbit stability is maintained by a balance between its kinetic energy and gravitationa

Analyzing the Transition from Circular to Elliptical Orbits

Design a simulation-based experiment to analyze how a slight increase in the orbital speed of a sate

Ball on a String Dynamics

A ball of mass $$m = 0.2\,kg$$ is attached to a string of length $$L = 1.5\,m$$ and is swung so that

Centrifuge Dynamics

A laboratory centrifuge spins a sample in a tube along a circular path of radius $$r$$ at a constant

Comparative Analysis of Gravitational and Centripetal Forces

In a laboratory experiment, a student attempts to compare the gravitational force acting on a suspen

Comparing Effects of Circular Motion and Gravitational Orbits

A satellite orbits a planet while an object is undergoing uniform circular motion in a laboratory. A

Crank-Driven Oscillatory System

A mechanical system uses a rotating crank to drive a piston. The crank has a radius of $$r = 0.1 \;m

Designing a Controlled Experiment to Distinguish Gravitation from Electromagnetism

A scientist wishes to design an experiment to distinguish gravitational forces from electric forces

Determining Angular Speed from Tangential Speed

A rotating disc has a marked point on its edge, and its tangential speed is measured directly. Use t

Effect of Charge Distribution on Electrostatic Force

In an experiment, two charged spheres are placed at varying separations, and the force between them

Electric Force Experiment Analysis

In an experiment, two charged spheres interact with each other. The electric force between them is e

Estimating the Required Charges for Equilibrium in a Charged Rotating System

A system consists of two small charged spheres that rotate about a common center. The only force pro

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 Centripetal Force using a Conical Pendulum

Design an experiment using a conical pendulum to investigate the relationship between the pendulum’s

Liquid Spinning Experiment Analysis

In a laboratory experiment, a cylindrical container with a radius of $$0.5 \;m$$ is filled with liqu

Mass Dependence in Centripetal Force

Two objects with different masses are attached to identical strings and swung in circular motion at

Radius Change and its Effect on Centripetal Acceleration

A car travels at a constant speed of 20 m/s around a circular track. Answer the following:

Satellite Orbit Calculation

A satellite orbits a planet in a uniform circular orbit. (a) Derive an expression for its orbital sp

Satellite Orbital Mechanics

A small satellite of mass $$m = 500\,kg$$ is in a circular orbit around a planet of mass $$M = 5.97

Spinning Ice Skater's Arms

An ice skater rotates with arms extended. With arms extended, the hand moves with a linear speed of

Uniform Circular Motion of a Car

A car with mass $$m = 1200 \;kg$$ moves at a constant speed of $$v = 20 \;m/s$$ around a circular tr

Analysis of Braking Work in a Car Deceleration

A researcher investigates the deceleration process of a car. A car of mass $$m = 1200 \; kg$$ is tra

Assessing the Impact of Air Resistance on Projectile Mechanical Energy

A projectile of mass 0.5 kg is launched horizontally from a cliff. Its speed is measured at various

Complex Analysis of Work in Variable Force Fields

A variable force given by $$F(x)= 20 + 4*x$$ (in N) is applied to a cart over a displacement of 5 m.

Comprehensive Analysis of a Rube Goldberg Machine

A Rube Goldberg machine is designed to complete a simple task through a series of energy transfer st

Determination of Power Output in a Vertical Lift

A researcher measures an athlete’s performance lifting a 50 kg weight vertically upward by 2 m in 5

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

Determining the Efficiency of a Simple Machine

Students design an experiment using a pulley system to lift a load. The input work (force times disp

Determining Work of Friction in a Sled on Snow

A 15 kg sled is sliding on snow with a coefficient of kinetic friction of 0.1. The sled slows from 4

Effect of Nonconservative Forces on Energy Conservation

A 2 kg block slides down a rough inclined plane, starting from rest, over a distance of 3 m, with fr

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

Evaluating the Effects of Surface Texture on Frictional Work

Design an experiment to determine how different surface textures affect the work done by friction on

Exploring Conservation of Mechanical Energy in Bouncing Ball Dynamics

A ball is dropped from a set height and allowed to bounce multiple times on a hard surface. The peak

Forces and Energy in a Bicycle Ride

A cyclist with a total mass (including the bicycle) of $$80\,kg$$ rides uphill and gains a vertical

Interpreting a Diagram of Mechanical Energy Conservation

A diagram is provided that shows the energy transformations of a roller coaster car as it moves alon

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

Mechanical Energy in a Roller Coaster

A roller coaster car of mass $$800 kg$$ starts from rest at the top of a hill $$30 m$$ high. Answer

Nonconservative Forces and Mechanical Energy Loss

A 4 kg block slides down a 15 m long ramp inclined at 30° to the horizontal. The block starts from r

Nonconservative Forces in a Skater's Motion

A 60 kg skater is observed decelerating from 8 m/s to 4 m/s over a distance of 20 m on a rough ice s

Pendulum Energy Conservation and Nonconservative Forces

In this experiment, a student sets up a pendulum and measures its maximum height and the speed at it

Potential Energy Variation in a Multi-Level Building

An elevator travels in a building that has floors at 0 m (ground), 3 m (first floor), and 18 m (top

Pulley System Energy Analysis

In a pulley system, a 50 kg mass is lifted 3 m vertically. Due to friction in the pulley, an extra 1

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 Power in a Jump

An athlete of mass 70 kg jumps upward and reaches a peak height of 0.8 m. The take-off time is measu

Work Done Along Different Paths

A cart is moved from point A to point B by applying a constant force of 50 N. Two paths are availabl

Work Done by a Variable Force

In an experiment, a cart is subjected to a variable force along its displacement. A graph of force v

Work Done by Friction on a Sliding Block

A 2 kg block is sliding on a rough horizontal surface and comes to a stop due to kinetic friction. T

Work Done by Variable Forces

A variable force is applied to an object as it moves along a straight line. The force as a function

Work Done in Circular Motion

A 1 kg ball tied to a string is moving in uniform circular motion at a constant speed of 5 m/s in a

Work Done with an Angled Force

A worker applies a force to move a crate along a horizontal surface in two different scenarios. Refe

Work-Energy Analysis in a Variable-Mass System

In an advanced experiment, a student investigates the work-energy theorem using a cart that loses ma

Work-Energy Theorem and Friction

Analyze the provided experimental data related to a block sliding on a rough surface. Use the data t

Work-Energy Theorem and Kinetic Energy

A 3 kg block is moving along a frictionless surface. Due to a constant force acting over a displacem

Work-Energy Theorem in a Kinetic Friction Scenario

A $$2\;kg$$ block slides across a rough surface. It starts with an initial velocity of $$5\;m/s$$ an

Analysis of a Perfectly Inelastic Collision

Consider a 2.0 kg cart moving at 4.0 m/s that collides with a 3.0 kg cart at rest, and the two carts

Assumption of Perfect Elasticity without Considering Collision Deformation

In this experiment, bouncy balls collide on a hard surface and their velocities are measured to stud

Assumption of Uniform Mass Distribution in a Pendulum Collision

In this experiment, a pendulum bob is released from a fixed height to collide with a stationary targ

Basic Momentum and Impulse: Data Analysis

In an experiment, three objects with differing masses and velocities were launched horizontally. The

Coefficient of Restitution in Collisions

A 1.0 kg ball moving at 8 m/s collides head-on with a 1.0 kg ball moving at -2 m/s. After the collis

Comparing Elastic and Inelastic Collisions

Two objects with masses $$m_1 = 4\,\text{kg}$$ and $$m_2 = 6\,\text{kg}$$ are moving on a frictionle

Conservation of Momentum in Two-Dimensional Collisions

In a frictionless ice rink, two pucks collide. Puck A has a mass of $$0.5$$ kg and moves east at $$4

Designing a Controlled Experiment for Elastic Collisions

Design an experiment to investigate the effect of varying mass ratios on the coefficient of restitut

Evaluating Momentum in Multi-Stage Collisions

A system of three objects (A, B, and C) on a frictionless track undergoes sequential collisions. Dat

Explosive Fragmentation and Momentum Conservation

A stationary projectile of mass $$12\,\text{kg}$$ explodes into three fragments. Fragment 1 has a ma

Force-Time Graph with Multiple Intervals

An object's force–time graph has three intervals: from $$0\,s$$ to $$1\,s$$ the force is constant at

Impulse Applied to Varying Masses

In a physics lab, a constant impulse of $$10$$ Ns is applied separately to two objects of different

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 Investigation

A researcher observes an inelastic collision in which two vehicles collide and stick together. The e

Investigating the Coefficient of Restitution

A 0.3 kg ball is dropped from a height of 2.0 m and bounces to a height of 1.2 m. The contact time w

Misapplication of the Impulse-Momentum Theorem in a Rotational Setup

In this experiment, a rotating wheel is subjected to a brief, linear force impulse and sensors recor

Misinterpretation of Force-Time Graph in Impulse Determination

In this experiment, students used a force sensor to record data during an object’s collision and plo

Momentum Analysis in Vehicle Collisions

In a car accident reconstruction, two vehicles with masses of 1500 kg and 1200 kg are involved. Afte

Momentum and Energy in a Diver's Jump

A diver with a mass of $$70\,kg$$ jumps off a platform and enters the water at a speed of $$3.0\,m/s

Momentum and Safety Design in Car Crashes

Modern cars use design features like airbags and crumple zones to manage the impulse experienced dur

Momentum Change Due to Friction

A 5.0 kg block is sliding on a horizontal surface and comes to rest due to kinetic friction over a p

Momentum Change in a Two-Collision Experiment

In a laboratory collision experiment on a low-friction track, two carts undergo sequential collision

Momentum Conservation in a Two-Car Collision

A scenario involving two cars colliding at a right angle is provided. Use conservation of momentum t

Momentum in Frictional Collisions

A researcher investigates collisions on a rough surface, where friction affects the momentum of slid

Momentum in Rotational Collisions

A uniform rod of length $$L = 2$$ m and mass $$M = 4$$ kg is pivoted at one end and is initially at

Momentum-Time Graph Interpretation

A momentum vs. time graph for a moving object is provided below. Analyze the graph to determine the

Multi-Stage Cart Collision

Three carts are placed on a frictionless track. Cart A (1.0 kg) is moving at 4.0 m/s toward Cart B (

Over-Simplified Analysis of Two-Dimensional Collisions

In this experiment conducted on an air table, two pucks undergo a two-dimensional glancing collision

Post-Collision Velocity Determination

In a laboratory experiment, two objects collide and separate. The masses and velocities of the objec

Rocket Launch Momentum Analysis

A rocket initially at rest has a total mass of $$500 \ kg$$. It ejects $$50 \ kg$$ of fuel at a velo

Rocket Propulsion and Momentum Conservation

A stationary spaceship of mass $$M = 1000\,\text{kg}$$ ejects a mass of fuel $$m = 50\,\text{kg}$$ a

Two-Dimensional Collision of Skaters

Two ice skaters participate in an experiment. Skater A (mass $$50\,kg$$) moves at $$2\,m/s$$ at an a

Analyzing Force vs. Displacement Graph in a Spring System

A force vs. displacement graph was generated for a spring system. Analyze the graph to determine if

Application of SHM in Real-World Systems

Many real-world systems, such as vehicle suspension systems, seismographs, and clock mechanisms, rel

Application: SHM in Seismology

In seismology, mass-spring systems are used as seismometers to detect ground motion. Consider a seis

Comparative Analysis of Mass-Spring and Pendulum Systems

Compare the oscillatory behavior of a mass-spring system and a simple pendulum. (a) Write down the

Comparing SHM Parameters in Different Media

A pendulum was oscillated in two different media: air and a viscous fluid. The table below lists the

Derivation of Acceleration in SHM from Newton's Second Law

Derive the acceleration expression for a system undergoing simple harmonic motion using Newton's Sec

Designing an SHM Experiment

Design an experiment to study the effect of varying the spring constant (k) on the period (T) of a m

Determining System Parameters from SHM Equations

A researcher is given an equation for the displacement of a mass-spring system: $$x = 0.05 \cos(25t

Determining the Spring Constant Using Force Measurements

A researcher measures the force required to displace a spring from its equilibrium position. The fol

Effect of Spring Constant on Oscillation

The spring constant (k) affects the angular frequency and period of oscillation in a mass-spring sys

Estimating the Spring Constant from SHM Data

An experiment is performed with a mass-spring system where different masses produce different oscill

Forced Oscillations and Resonance

A mass-spring system is subjected to an external periodic driving force described by $$F = F_0*\cos(

Hooke’s Law Lab Analysis

In a laboratory experiment, a spring is stretched by attaching various weights and the following dat

Mass-Spring Oscillator: Energy Analysis

An experiment is conducted with a mass attached to a horizontal spring on a frictionless surface. Th

Mathematical Modeling of SHM

Develop a mathematical model for the displacement of a harmonic oscillator.

Measurement Uncertainty in SHM Parameters

A student performs an experiment to measure the period, amplitude, and angular frequency of a mass-s

Pendulum Motion and Approximations

Consider a pendulum used in a clock, for which the period is given by $$T = 2\pi \sqrt{L/g}$$. This

Resonance in Driven Damped Oscillators

A driven, damped oscillator is described by the equation $$m\frac{d^2x}{dt^2}+b\frac{dx}{dt}+kx=F_0\

SHM and Gravitational Effects in Pendulums

Gravity plays a crucial role in pendulum motion as described by the equation $$T = 2π\sqrt{L/g}$$. A

Simple Harmonic Motion in Biological Systems

Biological systems, such as the rhythmic beating of a heart or neuron firing patterns, sometimes exh

Analyzing a Yo-Yo's Rotational and Translational Motion

A yo-yo exhibits both rotational and translational motion as it unwinds. Using the provided data, an

Analyzing Rotational Motion in Celestial Bodies

Astronomers have measured the angular velocities of stars at various distances from the center of a

Analyzing the Impact of Applied Force Angle on Torque

The effectiveness of an applied force in producing torque depends on the angle at which the force is

Angular Displacement from Arc Length Measurements

A small robot moves along a curved path that is part of a circle with a radius of $$r = 0.5\,m$$. It

Angular Displacement Measurement Using Encoders

A robotics engineer uses an optical encoder to measure the angular displacement of a robot arm. The

Bicycle Wheel Dynamics

A cyclist's bicycle wheel is modeled as a thin hoop having a mass of 2 kg and a radius of 0.35 m. Wh

Center of Mass in a Rotating System

A system consists of a uniform rod and two attached masses located at specified distances from a piv

Center of Mass in an Irregular Rotating Object

A researcher studies an irregularly shaped rotating object and claims that the object rotates about

Center of Mass in Rotating Systems

Design an experiment to study how the distribution of mass affects the location of the center of mas

Comparative Analysis of Rotational Motion in Different Systems

Two systems—a disc and a rod—are subjected to the same net torque. Their moments of inertia and corr

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

Determining Angular Acceleration in Non-Uniform Circular Motion

A rotating system exhibits non-uniform circular motion. Analyze the provided graph to determine both

Energy Considerations in Rotational Motion

An experiment measures both the rotational and translational kinetic energies of a rolling object. T

Evaluating Torque Using the Right-Hand Rule

A uniform rod is pivoted at one end. Forces are applied at different angles relative to the rod. In

Experimental Analysis of Rotational Deceleration

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

Force Distribution on a Rotating Beam

In this problem, you will analyze torques produced by weights attached to a beam and determine the a

Interpreting a Rotational Motion Schematic

Examine the provided schematic diagram of a rotating system. The diagram shows a disc rotating about

Measuring Frictional Torque

Develop an experimental design to determine the frictional torque acting on a rotating apparatus. Yo

Moment of Inertia and Rotational Kinetic Energy

Different objects are rotating with various moments of inertia and angular velocities. Use the data

Torque and Angular Momentum in a Rotating Machine

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

Torque Measurement Error in a Wrench Experiment

In a practical experiment using a wrench to measure torque on a bolt, a student applies force at var

Torque Requirements in a Robotic Arm

Design a robotic arm joint system where motors are required to generate sufficient torque for rotati