A wheel rotating with a constant angular acceleration turns through 23 revolutions during a 3 s time interval. Its angular velocity at the end of this interval is 16 rad/s. What is the angular acceleration of the wheel

Answer

Given,

Revolution of wheel = 23 rev.

                                  = 23 x 2π = 46 π

Time = 3 s

final angular velocity = 16 rad/s

angular acceleration of wheel = ?

Now, Calculating the initial angular speed of the wheel

Angular displacement = (initial velocity + final velocity) x time.

now, angular acceleration

Hence, the angular acceleration of wheel is negative means wheel is decelerating.

- 21.4 rad/s²

Explanation:

number of turn, n = 23

angle turned, θ = n x 2π = 23 x 2 x π = 46 π rad

time, t = 3 s

final angular velocity, ω = 16 rad/s

Let the initial angular velocity is ωo.

Angular displacement = Average angular velocity x time

46π  x 2 = (16 + ωo) x 3

ωo = 80.3 rad/s

Let α is the angular acceleration, by use of first equation of motion for rotational motion

16 = 80.3 + α x 3

α = - 21.4 rad/s²

The angular acceleration of the wheel is - 21.4 rad/s².

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