Rotational Dynamics
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 = mr 2 α |
| 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 = 
Iσ
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 =
mσ
2
r
2 +
Iσ
2
|
| Formula for the moment of inertia of a rigid body |
I =
r
2
dm
|
