The uniform circular disk of 200-mm radius has a mass of 25 kg and is mounted on

Question

The uniform circular disk of 200-mm radius has a mass of 25 kg and is mounted on the rotating bar OA in three different ways. In each case the bar rotates about its vertical shaft at O with a clockwise angular velocity cu0 4 rad/s. In case (a) the disk is welded to the bar. In case (6) the disk, which is pinned freely at A, moves with curvilinear translation and therefore has no rigid-body rotation. In case (c) the relative angle between the disk and the bar is increasing at the rate theta = 8 rad/s. Calculate the angular momentum of the disk about point O for each case.

Explanation / Answer

Given data:

R1 = 200 mm

R2 = 400 mm

M = 25 Kg

Solution a)

To find the angular momentun of the disk about the point O, we have that:

Firts, to get moment of inertia of system

I = I1

I1 = M*R2^2 = 4

I = 4 Kgm^2

So, The angular moment is:

L = I*w = 4*4

L = 16

Solution b)

To find the angular momentun of the disk about the point O, we have that:

Firts, to get moment of inertia of system

I = I1 + I2

I1 = (1/2)*M*R1^2 = 0.5

I2 = M*R2^2 = 4

I = 4.5 Kgm^2

So, The angular moment is:

L = I*w = 4.5*4

L = 18

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