Question

A weather vane initially at rest has a moment of inertia of 0.105 kg · m² about its axis of rotation. A 64.0 g piece of clay is thrown at the vane and sticks to it at a point 10.0 cm from the axis. The initial velocity of the clay is 16.5 m/s, directed perpendicular to the vane. Find the angular velocity of the weather vane just after it is struck.

Answer 1

First you find your initials

Since the clay is the only thing moving initially, you only do the formula for the clay

so:

I_i = MR^2= (0.064kg)(0.1m)^2 = 0.00064 kg-m^2

w_i = (V/r)= 16.5/0.1= 165 rad/s

For your finals

Since the clay stuck to the vane, they have the same angular velocity so you can write the angular momentum as

I_f = I(vane) + I(clay)) = 0.105 + 0.00064 = 0.10564 kg-m^2

By conservation of angular momentum:

I_i w_i = I_fw_f

0.00064*165 = 0.10564 w_f

=> w_f = 0.9996 rad/s