A turntable has 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 very small and very light cup-shaped mechanism on the rim of the turntable (see figure).What is the angular velocity of the turntable just after the ball is caught? A) 2.1 rad/s B) 1.3 rad/s C) 0.94 rad/s D) 0.75 rad/s E) 0.30 rad/s

Question

Quizplus · Accepted Answer

We can use conservation of angular momentum to solve for the final angular velocity of the turntable after the ball is caught. 
Initial angular momentum = final angular momentum 
Initial angular momentum of turntable = Iω 
where I is the moment of inertia of the turntable and ω is the initial angular velocity of the turntable. 
Final angular momentum of turntable and ball = (I + mr²)ω'
where m is the mass of the ball, r is the radius of the turntable, and ω' is the final angular velocity of the turntable. 
Initial angular momentum = Final angular momentum 
Iω = (I + mr²)ω' 
ω' = (Iω)/(I + mr²) 
Substituting the given values, we have: 
ω' = (2.0 kg•m²•1.5 rad/s)/(2.0 kg•m² + 0.40 kg•(0.80 m)²) = 1.3 rad/s 
Therefore, the angular velocity of the turntable just after the ball is caught is 1.3 rad/s.

A Turntable Has a Radius of 0