Need help with Question 8 please. the cup overflows. the cup might overflow but

Question

Need help with Question 8 please.

the cup overflows. the cup might overflow but it depends on the actual mass of the ice cube. the water level remains the same. the water level actually goes down. There is not enough information to answer this question. A wheel has a radius of 0.40 m and is mounted on frictionless bearings. A block is suspended from a rope that is wound on the wheel and attached to it (see figure). The wheel is released from rest and the block descends 1.5 m in 2.00 s without any slipping of the rope. The tension in the rope during the descent of the block is 20 N. What is the moment of inertia of the wheel?

Explanation / Answer

d = 1/2 * a * t2

a = 2 * d / t2

alpha = a/R

As the rope is perfectly perpendicular to the wheel radius, the cross product turns in to simple multiplication, and honestly we don't care about the vector direction of tau.

tau = T * R

tau = I * alpha

T * R = I * 2 * d / ( t2 * R)

I = T * R2 * t2 / (2*d) = 20 * 0.42 *  22 / (2*1.5)

I = 4.27 kg.m2

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