Section 8
Rotation
Derivative of angular velocity with respect to time.
Angular velocity with constant angular acceleration.
Angular position with constant angular acceleration.
Relation between angular velocities and angular displacement, without explicit time.
Sum of the products of each point mass and the square of its distance to the axis.
Integral of the square of the distance to the axis with respect to mass.
The moment of inertia about a parallel axis is that about the center of mass plus Md².
Magnitude
Torque is the cross product of the position vector and the force.
The net torque is the product of the moment of inertia and the angular acceleration.
Kinetic energy associated with rotation, equal to one-half Iω².
Equivalent form
Total kinetic energy
In rolling without slipping, the center-of-mass speed is Rω and the kinetic energy includes translation and rotation.
The angular momentum of a particle is the cross product of position and linear momentum.
The angular momentum of a rigid body about a fixed axis is Iω.
The net external torque is the derivative of angular momentum with respect to time.
For a body whose moment of inertia changes
The initial angular momentum equals the final angular momentum.
- zero net external torque.