Explanation:
It is given that,
Force on grindstone, F = 180 N
Radius of grindstone, r = 0.28 m
Mass of grindstone, m = 75 kg
We need to find the angular acceleration of the grindstone. In rotational motion, the relation between the torque and angular acceleration is given by :
[tex]\tau=I\times \alpha[/tex]
[tex]\alpha=\dfrac{\tau}{I}[/tex]
I is the moment of inertia of solid disk, [tex]I=\dfrac{1}{2}mr^2[/tex]
[tex]\tau[/tex] is the torque exerted, [tex]\tau=F\times r[/tex]
[tex]\alpha=\dfrac{F\times r}{\dfrac{1}{2}mr^2}[/tex]
[tex]\alpha=\dfrac{2F}{mr}[/tex]
[tex]\alpha=\dfrac{2\times 180\ N}{75\ kg\times 0.28\ m}[/tex]
[tex]\alpha =17.14\ rad/s^2[/tex]
So, the angular acceleration of the disk is [tex]17.14\ rad/s^2[/tex]. Hence, this is the required solution.
