The cylinder rotates about the fixed z-axis in the direction indicated. if the speed of point a is va = 2.7 ft/sec and the magnitude of its acceleration is aa = 20.6 ft/sec2, determine the magnitudes of the angular velocity and angular acceleration of the cylinder. is knowledge of the angle θ necessary?

7.63 rad / s

58.2 rad/s^2

Explanation:

v = 2.7 ft/s

a = 20.6 ft/s^2

Let w be the angular velocity and r be the radius of cylinder.

As we know that

v = r w

a = r w^2

So,

2.7 = r w (1)

20.6 = r w^2   (2)

Divide equation (2) by equation (1), we get

20.6 / 2.7 = w

w = 7.63 rad / s

Put in equation (1)

r = 2.7 / 7.63 = 0.354 ft

Angular acceleration = a / r = 20.6 / 0.354 = 58.2 rad/s^2

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