A turntable has rotational inertia I and is rotating with angular speed about a

Question

A turntable has rotational inertia I and is rotating with angular speed about a frictionless vertical axis. A wad of clay with mass m is tossed onto the turntable and sticks a distance d from the rotational axis. • First find the new angular speed if the clay was tossed straight down. • Now find the new angular speed if the clay hits the turntable horizontally with its velocity vector at right angles to the turntable’s radius in the same direction as the original rotation. Use v for the speed of the clay.

Explanation / Answer

w' = new angular speed

I' = moment of inertia of clay = md2

using conservation of angular momentum

I w = (I + I') w'

I w = (I + md2) w'

w' = I w /(I + md2)

Case 2 :

new angular momentum = initial angular momentum of turntable + initial angular momentum of clay

(I + md2) w' = I w + mvd

w' = (I w + mvd)/(I + md2)

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