Answer:
w_f = m*V*cos(Q_n) / L*(m+M)
Explanation:
Given:
- mass of the putty ball m
- mass of the rod M
- Velocity of the ball V
- Length of the rod L
- Angle the ball makes before colliding with rod Q_n
Find:
What is the angular speed ωf of the system immediately after the collision,
Solution:
- We can either use conservation of angular momentum or conservation of Energy. We will use Conservation of angular momentum of a system:
L_before = L_after
- Initially the rod is at rest, and ball is moving with the velocity V at angle Q from normal to the rod. We know that the component normal to the rod causes angular momentum. Hence,
L_before = L_ball = m*L*V*cos(Q_n)
- After colliding the ball sicks to the rod and both move together with angular speed w_f
L_after = (m+M)*L*v_f
Where, v_f = L*w_f
L_after = (m+M)*L^2 * w_f
- Now equate the two expression as per conservation of angular momentum:
m*L*V*cos(Q_n) = (m+M)*L^2 * w_f
w_f = m*V*cos(Q_n) / L*(m+M)