Question

A wheel rotating with a constant angular ac-celeration turns through 17 revolutions duringa 4 s time interval. Its angular velocity at theend of this interval is 14 rad/s.What is the angular acceleration of thewheel? Note that the initial angular velocity isnotzero.

Answer 1

Answer:

α = 1.375 rad/s²

Explanation:

given,

wheel rotate 17 revolution in time t = 4 s

angular velocity at the end,ω = 14 rad/s

angular acceleration of the wheel = ?

we know,

1 revolution = 2 π rad

17 revolution = 34 π rad

initial angular speed = $\dfrac{34\pi}{4}$

                               ω₀ = 8.5 π rad/s

now, using equation of rotational motion to calculate angular acceleration

$\omega = \omega_0 + \alpha t$

$14 =8.5+ \alpha\times 4$

           4α = 5.5

          α = 1.375 rad/s²

Hence, angular acceleration of the wheel is equal to α = 1.375 rad/s²