ROTATION II

I. An object rotating about a fixed axis O has rotational Kinetic Energy.

A. For a particle of mass m, the KE is (1/2)mv2.

B. How is this modified for a rotating object consisting of many particles?

C. What is rotational inertia?

D. What is the expression for rotational KE in terms of rotational inertia and the angular speed?

E. Note that the rotational inertia I depends on the mass of the object and the distribution of the mass relative to the axis of rotation.

F. Generally I can be found in tables and is often given for an axis through the center of mass.

G. If the axis is not through the center of mass how can the rotational inertia be found?

II. If a particle is at a position denoted by the vector r as measured from an origin and a force F acts on it, how do we define the torque? (Note that torque is a vector.)

A. What is the magnitude of the torque?

B. What is the right-hand rule?

III. If a particle is at a position denoted by the vector r as measured from an origin and has a momentum p, how do we define the angular momentum? (Note that angular momentum is a vector.)

A. What is the magnitude of the angular momentum?

B. Use the right-hand rule again.

IV. What is the connection between torque and angular momentum?

V. How do we determine the work energy done on rotating objects?

VI. How is rotational KE related to the work done?

VII. What is Newton's Second Law for rotating objects?

VIII. When is the angular momentum a constant in time?

Example

A 10 gram bullet with a speed of 300 m/s strikes a block on the edge of a horizontal disk of radius 0.50 m. If the disk can pivot about a vertical axis through its center and the rotational inertia of the disk-block assembly is 4.0 kg-m2, determine the final angular speed of the disk if it was not moving when the bullet struck the block.