Question

A solid cylinder of mass 3.0 kg and radius 1.0 m is rotating about its axis with a speed of 40 rad s-1. Calculate the torque which must be applied to bring it to rest in 10s. What would be the power required?

Answer 1

Answer on Question #65704, Physics / Mechanics | Relativity |

A solid cylinder of mass $3.0\,\mathrm{kg}$ and radius $1.0\,\mathrm{m}$ is rotating about its axis with a speed of 40 rad/sec. Calculate the torque which must be applied to bring it to rest in 10 sec. What would be the power required?

Solution

$$\begin{array}{l} m = 3\,\mathrm{kg} \\ R = 1\,\mathrm{m} \\ \omega_1 = 40\,\mathrm{rad/sec} \\ \omega_2 = 0 \\ t = 10\,\mathrm{sec} \\ \tau - ?,\, F - ? \\ \tau = I \frac{d\omega}{dt} = I \frac{\omega_1 - \omega_2}{t},\ I = \frac{m R^2}{2} \\ \tau = \frac{3 \cdot 1}{2} \cdot \frac{40}{10} = 6(\mathrm{N \cdot m}) \\ \end{array}$$ $$F = \tau / R = 6 / 1 = 6\,(\mathrm{N})$$

Answer: $6\,\mathrm{N}\,\mathrm{m},\, 6\,\mathrm{N}$

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