Rotational Motion

Purely rotational motion means that all points are moving in a circle about an axis of rotation.

The angular position of a rotating object is specified with . This can be defined by the length of circumference moved by the radius of the circle:

If , then 1 rad. This means that .

The angular velocity is defined the same way linear velocity is:

Or with a derivative for instant angular velocity. This is usually in rads/s.

Similarly, for angular acceleration:

We can translate both of these to linear using:

because:

For both and , the magnitude may stay the same, but the direction will always be changing.

A spinning object also has a Centripetal Acceleration that points towards the axis, . We can rewrite this in terms of .

Because Centripetal Acceleration and our tangential acceleration are perpendicular, we can use them as components of linear acceleration:

We can also find using these two values. We can form a triangle:

Angular quantities are vectors, and to define their direction, we use the Right-hand Rule.

Right-hand Rule for Rotation

We can relate the frequency as angular velocity over distance:

Here are the angular Kinematic Equations.

Torque is a Force about an axis.

Rotational Inertia or Moment of Inertia is the rotation equivalent of mass.

Rotational Kinetic Energy

Angular Momentum

Angular Momentum and Angular Velocity

Precession

Rotational Kinetic Energy