Question

at t=0 a flywheel is rotating at 50 rpm angular acceleration of 0.5 rad / s2

Answer 1

Given:

At, t=0 a flywheel is rotating at 50 rpm angular acceleration of 0.5 rad /s^2.

To Find:

Find the time required to stop the flywheel ?

Solution:

It is given that-

at t=0 , initial angular speed is 50 rpm.

therefore,

$\omega_{0}=50 rpm=\dfrac{50}{60}=\dfrac{5}{6}rps$$=\dfrac{5}{6}(2\pi)=\dfrac{5\pi}{3}rad/s$

and final angular speed,  $\omega=0\ rad/s$

also, given that , angular acceleration is 0.5 rad/s^2.

since, final angular speed is 0.

∴  $\alpha = -0.5 \ rad/s^2$  

Now, from kinematics.

$\omega=\omega_{0}+\alpha t$

⇒   $t=\dfrac{\omega-\omega_{0}}{\alpha}$

$t=\dfrac{0-5\pi/3}{-0.5}\\\\=\dfrac{10\pi}{3}\\\\=3.34\pi$

Hence, 3.34π sec is required to stop the flywheel.