AP Physics 1: Torque and Angular Momentum

Armistead is goated

Newtons Second Law for Torques

ΣΤ = Iα, α = Στ/I, I = ΣΤ/α

Before calculating angular momentum, it is necessary to define a

Rotational Axis

Angular momentum for an extended object

L = Iω

Angular momentum for a point object

L = mvr 

Variable for angular momentum

L

Angular equivalent to mass

Rotational Inertia

Variable for rotational inertia

I

Angular equivalent of velocity

Angular velocity

Variable for angular velocity

ω

Units of rotational inertia

kg⋅m²

Units of angular velocity

rads/sec

Angular equivalent to displacement

Angular displacement

Variable for angular displacement

ΔΘ

Units of angular displacement

Radians

Angular equivalent to acceleration

Angular acceleration

Variable of angular acceleration

α

Units for angular acceleration

rads/sec/sec

Angular equivalent of force

Torque

Variable for torque

τ

Units of torque

N⋅m

Definition of torque

Τ = Fd⟂

Angular equivalent to momentum

Angular Momentum

Units of angular momentum

N⋅m⋅s

For an object moving in a straight line at a constant speed, r represents 

distance of closest approach 

When no torques act external to a system

angular momentum of the system cannot change

Angular momentum is a

vector

Angular momentum’s in the same sense

Add

Angular momentum’s in opposite senses 

subtract

Angular moment is conserved __________ from linear momentum

separately

Angular impulse-momentum theorem

τΔt = ΔL

Variable for angular impulse

ΔL

Units of angular impulse

N⋅m⋅s

A change in angular momentum equals

Net torque multiplied by the time the torque is applied

Equation for rotational kinetic energy

Kr = 1/2Iω²

Angular displacement indicates

the angle through which an object has rotated.

Average angular velocity ω is

angular displacement divided by the time interval over which that angular displacement occurred.

Instantaneous angular velocity is

how fast an object is rotating at a specific moment in time.

Angular acceleration αtells how much an objects

angular speed changes in one second.

Angular acceleration and centripetal acceleration are

Independent

Angular acceleration changes an objects __________ _____, while centripetal acceleration changes an objects _________ __ _______

Rotational speed, direction of motion

If rotating around a fixed axis or rolling without slipping, linear displacement is given by 

x = rΘ

If rotating around a fixed axis or rolling without slipping, linear speed is given by

v = rω

If rotating around a fixed axis or rolling without slipping, linear acceleration is given by

a = rα

A lever arm is

the perpendicular distance from the axis of rotation to the line of action of a force

Rotational inertia I represents an object’s resistance to

Angular acceleration

For two objects of the same mass, rotational inertia is higher if

the mass is distributed farther from the rotational axis

For a point particle, rotational intertidal is MR²

MR²

Rotational intertidal of multiple objects

add together algebraically

If you know an objects rotational intertidal about its center of mass, the rotational inertia about a parrallel axis  is given by 

I’ = I + Md²