A small block having mass m sits on a uniform disk that has radius R=0.5m. Initi

Question

A small block having mass m sits on a uniform disk that has radius R=0.5m. Initially the disk is rotating about an axis through its center such that the mass has speed v=0.5 m/s. The mass is located at a distance R/2 from the center of the disk and the disk has a moment of inertia I. At t=0 the system is given an angular acceleration ?=1.5 rad/s2 about the center of the disk.

(a) What is the initial angular velocity of the disk?

(b) What is the moment of inertia of the system about the center of the disk?

c) How many revolutions has the disk made between t=0s and the time the disk has an angular velocity of 4.5 rad/s?

Explanation / Answer

total moment of intertia = I + m(R/2)^2 = I + mR^2/4,

(c)w1=0.5/0.25=2,

w2=4.5,

(w2-w1)/alpha =t=> t=1.667sec

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