You spin a disk, giving it an initial angular velocity of 2.10 rad/s clockwise.

Question

You spin a disk, giving it an initial angular velocity of 2.10 rad/s clockwise. After you give it that initial spin, the disk has a constant angular acceleration of 0.800 rad/s2 counterclockwise.

(a) How much time passes before the disk reverses direction?

(b) Relative to its starting position, what is the disk’s angular displacement (in radians) at the instant it comes instantaneously to rest?

(c)  What is the disk’s angular velocity at = 11 sec. after you gave it its initial angular velocity? Use a positive sign for counterclockwise, and a negative sign for clockwise.

Explanation / Answer

w0 = -2.10 rad/s

alpha = 0.80 rad/s^2

(A) it reverse direction when w becomes zero.

wf= wi + alpha t

0 = - 2.10 + 0.80 t

t = 2.625 sec

(B) wf^2 - wi^2 = 2 alpha theta

0^2 - (-2.10)^2 = 2(0.80)(theta)

theta = 2.756 rad

(C) w = w0 + alpha t

w = - 2.10 + (0.8 x 11)

w = 6.7 rad/s

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