Question

A giant wheel of mass 250 kg having the diameter 5.0 m and plastic rope is set to enclose
around the wheel while the wheel is in motion and wheel is rotated by pulling the rope
off the wheel, find the magnitude of the constant force on the wheel from rest to an
angular speed of 0.500 rev/s in 5.00 s​

Answer 1

Given that :

It is given that,

Mass of wheel, m = 250 kg

The diameter of the wheel, d = 5 m

To find :

The constant force on the wheel from rest to an  angular speed of 0.500 rev/s in 5.00 s​.

Solution,

Let a is the angle acceleration such that :

$a =\dfrac{2\pi \times 0.5\ rad/s}{5\ s}\\\\a=0.62\ rad/s^2$

Let F is the force. So, force is given by :

$F=ma \\\\F=250\times 0.628\\\\F=157\ N$

So, the magnitude of the constant force is 157 N.