A uniform disk of mass M = 1.6 kg and radius R = 0.18 m rotates counterclockwise

ID: 2251399 • Letter: A

Question

A uniform disk of mass M = 1.6 kg and radius R = 0.18 m rotates counterclockwise at a constant rate of 36 rev/s about its central axis.

Determine the direction of the angular velocity vector.

Determine the tangential speed of a point 0.052 m from the center.

Determine the radial acceleration of a point on its rim.

Determine the total distance a point on the rim moves in 2.0 s.

If a bug of mass m = 0.050 kg walks outward from the center of the rotating

disk, what will be the angular speed of the disk when the bug gets to the edge?

counterclockwise w = 36 rev/sec = 72*pi rad/sec

2. V = wR1 = 36*2*pi * 0.052 = 11.76 m/s

alphaR = dw/dt

w = angular velocity = constant

radial acceleration = 0

theta = w*t + 0

theta = 72*pi*2 = 452.289 rad

5. I = 0.5 M R^2 = 0.02592

Inew = I + mR^2 = 0.02592 + 0.05 * 0.18^2 = 0.02754

conserving angular momentum

I * w1 = Inew * w2

w2 = 0.02592 * 72 * pi / 0.02754 = 212.889 rad/sec

w2 = 33.88 rev/sec

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