b. (5 points) What is the operational angular speed of the plate? 17(10 points)

Question

b. (5 points) What is the operational angular speed of the plate? 17(10 points) A turntable as a radius of 0.80 m and a moment of inertia of 2.0 kg-m2. The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings. A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s. The ball is caught by a cup-shaped mechanism on the rim of the turntable. What is the angular velocity of the turntable just after the ball is caught? 2.0 kg-m2 0.8 m 1.5 rad/s 3.0 m/s 0.4 kg

Explanation / Answer

Angular momentum I*w is conserved

Initial I*w = 2.0 * 1.5 kg.m^2/s = 3.0 kg.m^2/s = Final I*w

The moment of inertia of a point mass m rotating at radius r is m*r^2
= 0.4kg * 0.8^2 m^2
= 0.256 kg.m^2

So the total moment of inertia just after the ball is caught is 2.256 kg.m^2

So the new angular velocity is 3.0 / 2.256 rad/s = 1.33 rad/s

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