Question

A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 290 N applied to its edge causes the wheel to have an angular acceleration of 0.814 rad/s2.What is the mass of the wheel?

Answer 1

The mass of the wheel is 2159.045 kg

Step-by-step explanation:

Given:

Radius
`r = 0.330`

m

Force
`F = 290` N

Angular acceleration
`\alpha = 0.814 (rad)/(s^(2) )`

From the formula of torque,

Γ
`= I\alpha` (1)

Γ
`= rF` (2)

`rF = I \alpha`

Find momentum of inertia
`I` from above equation,

`I = (rF)/(\alpha )`

`I = (0.330 * 290)/(0.814)`

`I = 117.56`
`Kg. m^(2)`

Find the momentum inertia of disk,

`I = (1)/(2) Mr^(2)`

`M = (2I)/(r^(2) )`

`M = (2 * 117.56)/((0.330)^(2) )`

`M = 2159.045` Kg

Therefore, the mass of the wheel is 2159.045 kg