A wheel that was initially spinning is accelerated at a constant angular acceleration of 5.0 rad/s^2. After 8.0 s, the wheel is found to have made an angular displacement of 400 radians. (a) How fast was the wheel spinning initially? (b) What is the final angular velocity of the wheel?

Question

Physics

Kody

27 February, 13:22

A wheel that was initially spinning is accelerated at a constant angular acceleration of 5.0 rad/s^2. After 8.0 s, the wheel is found to have made an angular displacement of 400 radians. (a) How fast was the wheel spinning initially? (b) What is the final angular velocity of the wheel?

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Answers (1)

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Jase Wang · Answer 1

a) Initial angular speed = 30 rad/s

b) Final angular speed = 70 rad/s

Explanation:

a) We have equation of motion s = ut + 0.5at²

Here s = 400 radians

t = 8 s

a = 5 rad/s²

Substituting

400 = u x 8 + 0.5 x 5 x 8²

u = 30 rad/s

Initial angular speed = 30 rad/s

b) We have equation of motion v = u + at

Here u = 30 rad/s

t = 8 s

a = 5 rad/s²

Substituting

v = 30 + 5 x 8 = 70 rad/s

Final angular speed = 70 rad/s