Question

A wheel, starting from rest, rotates with a constant angular acceleration of 4.50 rad/s². During a certain 5.00 s interval, it turns through 85.0 rad.

(a) What is the angular velocity of the wheel at the start of the 5.00 s interval?
rad/s

(b) How long has the wheel been turning before the start of the 5.00 s interval?
s

Answer 1

Solution)

Part a)

We know,

Angular Displacement = (Initial Angular Velocity)t +

(1/2)(Angular Acceleration)t^2

θ = ωi(t) + (1/2)αt^2

85 rad = ωi(5.0s) + (1/2)(4.50rad/s^2)(5.0s)^2

ωi = 5.75 rad/sec

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Now, starting from rest, ωi = 0, and ωf = 5.75 rad/sec

with α = 4.5 rad/s^2. Hence,

α = (ωf - ωi)/t

t = 1.27 sec (Ans)

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