You\'ve been asked to help evaluate a proposal in which you try to build a devic

Question

You've been asked to help evaluate a proposal in which you try to build a device for determining the speed of a puck hit on an ice rink. The device consists of a bar resting on ice, fixed at one end and free to rotate horizontally. At the free end the rod has a small basket, such that it can capture the disk. The disc slides down the ice perpendicular to the bar and is caught in the basket that is initially at rest and then the rod rotates. The designers claim that knowing the length of the bar, the mass of the bar, the mass of the disk and the frequency of rotation of the bar and disc together, you can determine the speed of the disk when he moved across the ice.

Explanation / Answer

The concept here is conservation of angular momentum.

the angular momentum of the disc before getting into the basket = the agnular momentum of the basket + disc system after

the angular momentum of the disc before = m*v*L

this angular momentum is about the fixed end of the bar.

v being its velocity.

L being the length of the bar.

Now let w be the angular velocity of the disc + basket system.

and I be the moment of inerta of the system.

So their angular momentum will be = I*w

since frequency of rotation f is known,

w can be found out by the formula = w = 2*pi / f.

and moment of inertia of the system = (mass of disc)*L*L + (Mass of basket)*L*L + 1/3*(mass of the bar)*L*L

so:

m*V*L = I*w.

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