Question

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Answer 1

Answer:

SOLUTION

Angular velocity equals the relative linear velocity divided by the radius.

vb = va + ωr

ω = (vb − va) / r

The disc has angular velocity 50 rad/s and radius 2 m. So the linear velocity of point A is v = (50 rad/s) (2 m) = 100 m/s. The linear velocity of point C is v = (50 rad/s) (1 m) = 50 m/s. And the linear velocity of point B is -100 m/s.

The angular velocity of point A with respect to point C is:

ω = (100 m/s − 50 m/s) / (1 m)

ω = 50 rad/s

The angular velocity of point A with respect to point O is:

ω = (100 m/s − 0 m/s) / (2 m)

ω = 50 rad/s

The angular velocity of point A with respect to point B is:

ω = (100 m/s − -100 m/s) / (4 m)

ω = 50 rad/s