Rotary Motion

Rotation about an internal axis

Radian Measure

• Radian: the angle which subtends an arc on the circumference equal to the radius.
• 1 radian = 57.3 degrees
• 360 degrees (one revolution) = 2p radians
• Angle in radians equals arc distance divided by radius: q = d/r

Angular variables

• Angular displacement: (q) rotation through an angle about an axis
• Angular velocity: (w) change in angular position with respect to time: w = Dq/Dt
• Angular acceleration: (a) change in angular velocity with respect to time: a = Dw/Dt

Rotational Inertia

• A measure of how hard it is to rotate an object
• Depends on how mass is situated with respect to rotational axis
• Mass closer to axis is easier to rotate than mass at greater distance
• Moving axis or rearranging mass will change rotational inertia

Newton's 2nd Law for Rotation

• A net torque will produce angular acceleration
• Acceleration will be directly proportional to net torque and inversely proportional to rotational inertia of rotating object
• Angular acceleration is vector directed along axis of rotation

Precession

• A secondary rotation of the axis of a rotating body
• Caused by a torque from the force of gravity on a rotating body
• Examples: spinning bicycle wheel, earth's axis both precess