AP Physics 1 Full Review (Unit 5 - Unit 6)

Radian measure

s/r

Angular position

Measured by angle θ

Angular displacement

Change in θ (θ_f-θ_i)

Rigid Body

Each point rotates with the same change in θ

Angular Velocity Equation

ω_avg (rad/s) = Δθ / Δt (rad/sec)

Average rate at which angular position changes

Angular Acceleration Equation

α_avg (rad/s²) = Δω / Δt (rad/s²)

Connecting linear and angular displacement

Δs = rΔθ

Connecting linear and angular velocity

v = rω

Connecting tangential and angular acceleration

a_T = rα

Tangential Acceleration = linear (speed kind of)

Torque

When a force exerted on an object causes it to change rotational motion (turning effect)

When does force exert torque?

For Force to exert torque, there needs to be a component of the force that is perpendicular to the radius of rotation

The turning effect is dependent on __ distance?

radial

Torque equation

τ = Iα

τ = r_{perpendicular}F

τ = rFsinθ

Free body diagram vs Force diagram

FBD: represents all forces acting on COM

Force Diagram: SHows forces acting on rigid object at the point of contact (shape instead of dot)

Rotational Inertia

Resistance to change to rotation (I)

For rotational motion to change, torque must be exerted

Rotational Inertia Equation

I = mr²

I_total = Σ(mr²)_i

I_total = I_a + I_b

Rotational Inertia depends on:

mass, size, and distribution of mass

Coefficient of mass distribution

I = #mr²

# is given depending on mass distribution

Rigid bodies usually rotate about ___

Center of Mass

Parallel Axis Theorem

I’ = I_cm = Md²

d = distance to the new axis point (ex. spinning a ruler from the farther hole rather than the middle)

Translational Equilibrium

When F_NET = 0

Rotational Equilibrium

When τ_NET = 0

Calculating net torque with multiple forces

Add them

Directions in rotational kinematics

Usually (can choose):

Counterclockwise = +

Clockwise = -

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Add CCW torques and subtract CW torques for rotational equilibrium

Newton’s First Law regarding rotational motion

ω = constant if τ_NET = 0

Newton’s 2nd Law regarding rotational motion

α_system directly proportional to τ_NET

Rotational inertia for disk (uniform mass)

I_disk = (1/2)mr²

Acceleration of a massive pulley

α_system = (m₁-m₂)g / (1/2)m_pulley+m₁+m₂

Acceleration of massless (ideal) pulley

α_system = (m₁ - m₂)g / m₁+m₂

Solving multi-object systems with a massive pulley requires ___

Newton’s 2nd Law for rotational motion

Ideal Pulley

• Has no mass (doesn’t affect system’s inertia)

• Doesn’t disperse energy (No friction in axle)

• Doesn’t change rope tension as it goes over the pulley

• Assume tension is the same on both sides

Angular Impulse Equation

J = τt

Torque x time

Massive Pulley

• Has rotational invertía

• Some force goes into spinning, not just pulling objects

• Tension is different on each side of the rope

Reminder

Sum torques for rotating forces in system and set equal to Iα

Translational Motion

Object moving in 1 or 2 dimensions (COM Moving)

Rotational Kinetic Energy

Object moving but COM not moving

Linear Kinematics —> Rotational Kinematics

x —> θ

v —> ω

a —> α

m —> I (Rotational inertia)

Equation for rotational Kinetic Energy

K_rot = ½ Iω²

K_trans = ½ mv²

K_total =

K_total = K_trans + K_rot (Scalar)

“Rotational Analogs”

Rotational equivalents to linear

Rotating objects have __ energy

Kinetic

Work equation

W = τΔθ = ΔK

Area under a τ v θ graph

Area = work done (like F v d)

Work-Kinetic Energy Theorem

W = ΔK_rot

Angular Momentum equation

L = Iω (kgm²/s)

Change in Angular Momentum equation

ΔL = ΣτΔt = IΔω

Area under Angular Momentum v time graph (L v t)

Net Torque

Rolling Rigid Bodies

Has both K_trans and K_rot

K_total = ½ mv² + ½ Iω²

Rolling without slipping (x, v, and a of COM)

Δx_cm = rΔθ

V_cm = rω

a_cm = rα

Reminder

Rotating/rolling conserves energy (friction doesn’t dissipate energy in that case)

Systems with more I have more __ in rotational

K_total

K_trans < K_rot

Rolling with Slipping (Mechanical Energy)

Mechanical Energy_final < Mechanical Energy_initial

Velocity for orbiting satellite equation

v = Square root (GM/r)

M = mass of central body

Kinetic energy of a satellite is __

constant

Angular momentum in linear terms

L = rmvsinθ

Elliptical Orbits

• K_E changes

• GPE changes

• Mechanical Energy constant

• Angular momentum constant

Escape velocity equation

V_esc = Square root (2GM/r)

Not on equation sheet, derived