# Rotational Dynamics

## Terms and Formulae

terms Terms and Formulae

### Terms

Torque  -  The rotational analogue to force.
Moment of Inertia  -  The property of an object that dictates its angular acceleration.
Rolling Without Slipping  -  The special case of combined rotational and translational motion in which the part of the object in contact with the ground has zero velocity.

### Formulae

 Definition of torque τ = Fr sinθ

 Vector definition of torque τ = r×F

 Relation between τ and α τ = mr2α

 Rotational Analogue to Newton's Second Law τ = Iα

 Definition of work in angular motion W = τμ

 Integral definition of work in angular motion W = τdμ

 Definition of kinetic energy in angular motion K = Iσ2

 Definition of power in angular motion P = τσ

 Relation between linear and angular velocity when an object is rolling without slipping vcm = σr

 Kinetic energy when an object rolls without slipping, in terms of v K = mv2 + I Kinetic energy when an object rolls without slipping, in terms of σ K = mσ2r2 + Iσ2

 Formula for the moment of inertia of a rigid body I = r2dm