Question

‏A 50 - N x m torque acts on a wheel with a moment of inertia 150 kg x m² . If the wheel starts from rest , how long will it take the wheel to make one revolution ?

Answer 1

t = 6.17 s

Step-by-step explanation:

For a 1 revolution movement,
`\triangle \theta = 2\pi`

Torque,
`\tau = 50 Nm`

Moment of Inertia,
`I = 150 kg m^2`

If the wheel starts from rest,
`w_(0) = 0 rad/s`

The angular displacement of the wheel can be given by the formula:

`\triangle \theta = \omega_0 t + 0.5 \alpha t^2`................(1)

Where
`\alpha` is the angular acceleration

`\tau = I \alpha\\\alpha = (\tau)/(I) \\\alpha = 50/150\\\alpha = 0.33 rad/s^2`

To get t, put all necessary parameters into equation (1)

`2\pi = 0(t) + 0.5(0.33)t^2\\2\pi =0.5(0.33)t^2\\t^2 = (4 \pi)/(0.33) \\t^2 = 38.08\\t = 6.17 s`