Physics Vocabulary Review

Velocity-Time Graph Basics

Vertical axis indicates velocity; the speed of an object.

Horizontal axis, often time, indicates the moment of observation.

Direction of movement is indicated by the position relative to the horizontal axis:

Above axis: Object moves away from the detector.

Below axis: Object moves toward the detector.

Distance Traveled:

To calculate distance, determine the area between the velocity-time graph and the horizontal axis.

Cannot determine the exact distance from the detector from this graph.

Acceleration:

The slope of the velocity-time graph indicates acceleration.

Straight segments on the graph represent constant acceleration.

Static Fluids

Density:

Defined by the formula: \rho = \frac{m}{V}

Standard unit: kilograms per cubic meter (\text{kg/m}^3).

Other units: g/cm^3 for solids, g/ml for liquids, g/L for gases.

Note: 1 cm^3 = 1 ml.

Pressure:

Calculated using: P = \frac{F}{A}

Unit: Pascal (Pa); 1 \text{Pa} \equiv 1 \frac{N}{m^2} \equiv 1 \frac{kg}{ms^2}.

Pressure in a static fluid column: P = P_0 + \rho g y

Here, P_0 = pressure at the surface, \rho = fluid density, g = acceleration due to gravity, y = height above the surface.

Buoyant Force:

Given by: F_B = \rho V g

Where \rho = density of fluid, V = volume of displaced fluid.

Simple Harmonic Motion

Definition:

Motion where objects vibrate back-and-forth.

Key Concepts:

Amplitude (A): Maximum distance from the equilibrium position.

Period (T): Time for one full cycle of motion.

Frequency (f): Number of cycles per second.

Graphing:

Position-time graphs take a sine or cosine shape.

Position as a function of time x(t) expressed mathematically.

Dynamics:

The net force on an object increases linearly with distance from equilibrium, always directed toward the equilibrium position.

Average speed: Four amplitudes per period.

Examples:

Common examples include pendulums and masses on springs.

Period of a mass-spring system: T = 2\pi\sqrt{\frac{m}{k}} (m = mass, k = spring constant).

Period for a pendulum: T = 2\pi\sqrt{\frac{L}{g}} (L = length of pendulum, g = gravitational acceleration).

Rotational Motion (Momentum + Energy)

Angular Momentum (L):

For extended objects: L = I\omega; for point objects: L = mvr, where r is the distance from the axis.

Conservation:

Angular momentum remains constant in absence of external torques.

Angular Impulse:

Related to angular momentum: \tau (\Delta t) = \Delta L.

Types of Energy:

Rotational Kinetic Energy: KE_r = \frac{1}{2} I\omega^2, where I = rotational inertia, \omega = angular speed.

Position-Time and Displacement

To find speed, analyze the slope of the position-time graph:

A forwards slope indicates movement away from detector.

A backward slope indicates movement toward detector.

Instantaneous velocity is the slope at a specific point, while displacement measures total position change.

Orbits

In circular orbits:

Kinetic and gravitational potential energy are constant, total mechanical energy remains unchanged.

Angular momentum is also constant due to no external torques.

In elliptical orbits:

Kinetic energy varies, as does gravitational potential energy.

Gravitational Mass vs. Inertial Mass:

Both masses are equal; gravitational mass measures interactions based on gravity, while inertial mass is based on the net force and acceleration.

Conservation of Momentum

Collisions: Momentum is conserved when no external forces act on a system.

The momentum before an event equals the momentum after the event.

In two-body collisions, momentum vectors add algebraically.

Kinematics of Rotations

Angular Motion: Defined by angular displacement, angular velocity, and angular acceleration.

Equations for rotational kinematics are similar to linear motion equations but use angular variables.

Relationships between linear and angular motion demonstrated by equations:

v = r\omega, a = r\alpha.

Linear and angular acceleration equations resemble those of linear kinematics.

Equations of Motion for a Rolling Object

Rolling objects have unique equations for motion: distance, speed, and acceleration depend on both translation and rotation
v{cm} = r\omega; a{cm} = r\alpha, showcasing relationships between linear and rotational motion.

Energy Forms and Applications

Kinetic Energy, Gravitational Potential Energy, and Spring Potential Energy all have standard equations governing their calculations:

KE = \frac{1}{2} mv^2 ; PE = mgh; PE_{spring} = \frac{1}{2} kx^2.

Power quantifies energy change per unit time: Power = \frac{Work}{Time}.

Work is calculated as an area under force vs. displacement graphs.

Conservation of Energy

Total mechanical energy is conserved in the absence of non-conservative forces. Relevant in analyzing systems and collisions where energy exchange occurs without loss