An engineer is playing with a device to measure the speed of a hockey puck on ic

Question

An engineer is playing with a device to measure the speed of a hockey puck on ice. Her device consists of a thin rod of mass m with a small cup on the end, which can catch a hockey puck. The rod has a length l.The other end of the rod is attached to a pin in the ice so that it can rotate on the surface of the ice in a horizontal circle. The puck of mass, M, is fired in a straight line, perpendicular to the rod and when it is caught in the end of the stick the whole assembly (rod and puck) rotates at angular velocity, .
a) About what axis should we consider the conservation of angular momen-tum to understand the system?
b) Show that you can use the givens to obtain an expression for the puck’s initial velocity.
c) How does your expression change if you put the pivot at the center of the rod?

Explanation / Answer

(A) axis passing through the pin and perpendicular to the rod.

(B) Applying angular momentum conservation,

Li = Lf

m v L = (m L^2 + M L^2 / 3) w

v = (3m + M) w L / (3 m)

(C) then

m v L/2 = (m (L/2)^2 + M L^2 / 12) w

m v L / 2 = L^2 ( m / 4 + M / 12) w

m v/ 2 = L (3m + M) w / 12

v = (3m + M) w L / (6 m)

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