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Rotational Dynamics

Terms and Formulae

Introduction and Summary

Rotational Dynamics

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 = mr 2 α
 
Rotational Analogue to Newton's Second Law τ =
 
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 = 2
 
Definition of power in angular motion P = τσ
 
Relation between linear and angular velocity when an object is rolling without slipping v cm = σr
 
Kinetic energy when an object rolls without slipping, in terms of v K = mv 2 + I
 
Kinetic energy when an object rolls without slipping, in terms of σ K = 2 r 2 + 2
 
Formula for the moment of inertia of a rigid body I = r 2 dm

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