Question

A majorette in a parade is performing some acrobatic twirlings of her baton. Assume that the baton is a uniform rod of mass 0.120 kg and length 80.0 cm .

A. Initially, the baton is spinning about an axis through its center at angular velocity 3.00 rad/s . (Figure 1) What is the magnitude of its angular momentum about a point where the axis of rotation intersects the center of the baton?

B. With a skillful move, the majorette changes the rotation of her baton so that now it is spinning about an axis passing through its end at the same angular velocity 3.00 rad/s as before. (Figure 2) What is the new amplitude of the angular momentum of the rod about a point where the axis of rotation intersects the end of the baton?

Answer 1

Concepts and reason

The main concepts used to solve this problem are moment of inertia about a center of mass and angular momentum.

First, calculate the moment of inertia about a chosen axis of rotation Finally, then use the moment of inertia to calculate the angular momentum about this axis of rotation.

Fundamentals

The figure shows the spinning of the baton about an axis through its center of mass.

The expression for the moment of inertia about its center of mass is,

Here, is the moment of inertia about its center of mass, M is the mass of the baton, and L is the length of the baton.

The figure shows the spinning of the baton about an axis about the end.

The expression for the moment of inertia about the end of the baton is,

Here, is the moment of inertia about the end of the baton, M is the mass, L is the length.

The expression for angular momentum is,

Here, L is the angular momentum, I is the moment of inertia, and is the angular velocity.

(A)

The expression for the moment of inertia about a center of mass is,

Substitute for M and for L in expression .

The expression for angular momentum about a point where the axis of rotation intersects the center of a baton is,

Substitute for and for in expression .

(B)

The expression for the moment of inertia about the end of the baton is,

Substitute for M and for L in expression .

The expression for angular momentum about a point where the axis of rotation intersects the end of the baton is,

Substitute for and for in expression .

Ans: Part A

The angular momentum about a point where the axis of rotation intersects the center of baton is .