Question

Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 8.0 s, it rotates 35 rad.

(a) What was the angular acceleration during this time?
___ rad/S^2

(b) What was the average angular velocity?
____ rad/s

(c) What is the instantaneous angular velocity of the disk at the end of the 8.0 s?
____ rad/s

(d) Assuming that the acceleration does not change, through what additional angle will the disk turn during the next 5.0 s?
____ rad

Answer 1

Answer:

(a) 1.093 rad/s^2

(b) 4.375 rad/s

(c) 8.744 rad/s

(d)  67.845 rad

Explanation:

initial angular velocity, ωo = 0

time, t = 8s

angular displacement, θ = 35 rad

(a) Let α be the angular acceleration.

Use second equation of motion for rotational motion

$\theta =\omega _{0}t+\frac{1}{2}\alpha t^{2}$

By substituting the values

35 = 0 + 0.5 x α x 8 x 8

α = 1.093 rad/s^2

(b)  The average angular velocity is defined as the ratio of total angular displacement to the total time taken .

Average angular velocity = 35 / 8 = 4.375 rad/s

(c) Let ω be the instantaneous angular velocity at t = 8 s

Use first equation of motion for rotational motion

ω = ωo + αt

ω = 0 + 1.093 x 8 = 8.744 rad/s

(d) Let in next 5 seconds the angular displacement is θ.

$\theta =\omega _{0}t+\frac{1}{2}\alpha t^{2}$

By substituting the values

θ = 8.744 x 5 + 0.5 x 1.093 x 5 x 5

θ = 67.845 rad