ap physics rotational kinematics and torque

x=r(θ) definition

Position described in polar coordinates

x=r(θ) explanation

The x-position depends on the distance from the origin rrr, which itself depends on the angle θ\thetaθ. Used to describe paths where distance changes with angle.

x=r2(π) definition

Position evaluated at a specific angle.

x=r2(π) explanation

This means the radius r is evaluated when θ=π (180°). Often used when analyzing motion or geometry at a particular angle.

τ=r×F definition

Vector definition of torque.

τ=r×F explanation

Torque is the rotational effect of a force and depends on both the force and where it is applied relative to the axis of rotation.

τ=rFsinθ definition

Magnitude of torque.

τ=rFsinθ explanation

Only the component of force perpendicular to the lever arm causes rotation.

τ=Fd definition

Torque using lever arm distance.

τ=Fd explanation

d is the perpendicular distance from the pivot to the line of action of the force. This is the most common form used in AP Physics 1.

τ=Iα definition

Rotational version of Newton’s Second Law.

τ=Iα explanation

Torque causes angular acceleration, just like force causes linear acceleration.

I=mr2 definition

Moment of inertia of a point mass

I=mr2 explanation

Shows that rotational inertia increases with mass and with distance from the axis.

v=rω definition

Relationship between linear speed and angular speed.

v=rω explanation

Points farther from the axis move faster even though angular speed is the same.

a=rα definition

Tangential acceleration.

a=rα explanation

Angular acceleration causes linear acceleration along the circular path.

τ=Fr definition

Torque when force is perpendicular to the lever arm

τ=Fr explanation

This is a special case of τ=rFsin⁡θ when θ=90

T=mg+ma definition

Tension in a rope when an object accelerates upward

T=mg+ma explanation

tension must support weight and provide acceleration

ωavg​=Δθ​/Δt definition

Average angular velocity

ωavg​=Δθ​/Δt explanation

Measures how fast angular position changes over time

ω=ω0+αt definition

Angular velocity with constant angular acceleration

ω=ω0+αt explanation

Rotational version of v=v0+atv = v_0 + atv=v0​+at

ω2=ω02​+2αΔθ definition

Angular kinematics equation without time

ω2=ω02​+2αΔθ explanation

Used when time is unknown or unnecessary

I=21​mr2 (Disk) definition

Moment of inertia of a solid disk or cylinder

I=21​mr2 (Disk) explanation

Mass is distributed throughout the radius, reducing rotational inertia compared to a hoop

τ=Fℓ definition

Torque using lever arm length

τ=Fℓ explanation

ℓ is the perpendicular distance from pivot to force line

α=a/r definition​

Relationship between linear and angular acceleration

α=a/r explanation

Linear acceleration depends on distance from the axis.

θ=θ0​+ω0​t+21​αt2 definition

Angular position with constant angular acceleration.

θ=θ0​+ω0​t+21​αt2 explanation

Rotational equivalent of the standard kinematics position equation.

linear term x

rotational term θ

what is the definition of θ and x

position/angular position (radians)

linear term v

rotational term ω

what is the definition of ω and v

Velocity / angular velocity (rad/s)

linear term a

rotational term α

what is the definition of α and a

Acceleration / angular acceleration (rad/s²)

linear term F

rotational term τ

what is the definition of τ and F

torque and force

rotational newton’s second law equation

τnet​=Iα

the more torque, the more _

angular acceleration

large moment of inertia makes it harder to _

rotate

in an atwood’s problem, the heavier mass goes in what direction?

down

in an atwood’s problem, the lighter mass goes in what direction?

up

when m2>m1, T=?

m1<t<m2

when both masses are doubled but keep the same distance, the acceleration _?

halves

if both strings break, what do both masses do?

accelerate downwards at g

m2 mass equation when m2>m1

m2g-T=m2a

m1 mass equation when m2>m1

T-m1g=m1a

when m2>m1, the formula to find a is _?

a=(m2-m1)g/m1+m2