Part A What is the magnitude of the angular velocity of the wheel after the bloc

Question

Part A What is the magnitude of the angular velocity of the wheel after the block has descended 3.60 m A thin, light wire is wrapped around the rim of a wheel, as shown in Figure 1). The wheel rotates about a stationary horizontal axle that passes through the center of the wheel. The wheel has radius 0.190 m and moment of inertia for rotation about the axle of 0.490 kg·m2 . A small block with mass 0.350 kg is suspended from the free end of the wire. When the system is released from rest, the block descends with constant acceleration. The bearings in the wheel at the axle are rusty, so friction there does -7.75 J of work as the block descends 3.60 m rad/s Submit My Answers Give Up Figure 1 of!

Explanation / Answer

Here,

d = 3.6 m

I = 0.490 Kg.m^2

W = - 7.75 J

m = 0.350 Kg

let the angular velocity is w

v = 0.190 * w

Using conservation of energy

0.50 * m * v^2 + 0.50 * I * w^2 = total work done

0.50 * 0.350 * (0.190 * w)^2 + 0.50 * 0.490 * (w)^2 = 0.350 * 9.8 * 3.6 - 7.75

solving for w

w = 4.28 rad/s

the magnitude of angular velocity is 4.28 rad/s

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