You have a grindstone (a disk) that is 95.2 kg, has a 0.399 m radius, and is turning at 93 rpm, and you press a steel axe against it with a radial force of 19.6 N. (a) Assuming the kinetic coefficient of friction betweensteel and stone is 0.2, calculate the angular acceleration of thegrindstone.

angular acceleration is - 0.2063 rad/s²

Explanation:

Given data

mass m = 95.2 kg

radius r = 0.399 m

turning ω = 93 rpm

radial force N = 19.6 N

kinetic coefficient of friction μ = 0.2

to find out

angular acceleration

solution

we know frictional force that is = radial force * kinetic coefficient of friction

frictional force = 19.6 * 0.2

frictional force = 3.92 N

and

we know moment of inertia that is

γ = I * α = frictional force * r

so

γ = 1/2 mr²α

α = - 2f / mr

α = - 2 (3.92) / 95.2 (0.399)

α = - 7.84 / 37.9848 = - 0.2063

so angular acceleration is - 0.2063 rad/s²