A wheel rotating with a constant angular acceleration turns through 19 revolutions during a 3 s time interval. Its angular velocity at the end of this interval is 18 rad/s. What is the angular acceleration of the wheel? Note that the initial angular velocity is not zero. Answer in units of rad/s 2.

- 14.5 rad/s^2

Explanation:

n = 19

θ = 2 x 3.14 x 19 = 119.32 rad

t = 3 s, ω = 18 rad / s, ω0 = ?,

Let α be the angular acceleration.

Use First equation of motion for rotational motion

ω = ω0 + α t

18 = ω0 + α x 3

ω0 = 18 - 3α ... (1)

Use second equation of motion for rotational motion

θ = ω0 t + 1/2 x α x t^2

Put the value of ω0 = 18 - 3α from equation (1)

119.32 = (18 - 3α) x 3 + 1/2 x α x 9

119.32 - 54 = - 4.5 α

α = - 14.5 rad/s^2