Answer to Question #92525 in Mechanics | Relativity for Constantine

Question

A constant torque of 200N turns a wheel about its centre, the moment of inertia about this axis is 100kilogram meter square. Find the kinetic energy gained in 20 revolutions

Answer 1

Work W done by a constant torque

$$W=\tau\theta,\\ where\ \tau\ is\ torque\ and \ \theta\ is\ angular\ displacement$$

Angular displacement after 20 revolutions is

$$\theta=20\cdot2\cdot\pi rad=40\pi rad,$$

therefor

$$W=200Nm\cdot40\pi rad=8000\pi J\approx25132.74J.$$

According to Work-Kinetic theorem for rotation kinetic energy of the wheel

$$E_k=W=8000\pi J\approx25132.74J.$$

Answer: 25132.74J.