Answer to Question #102690 in Mechanics | Relativity for sakshi

Question

A centrifuge in the shape of a uniform cylinder of radius 20 cm and mass 10 kg cylinder is spinning about its axis at a speed of 50,000 rpm. Determine the torque that must be applied in order to bring the centrifuge to a stop in 20 s. Calculate the power dissipated.

Answer 1

Torque:

$$\tau=I\alpha=I\frac{\omega}{t}=0.5mr^2\frac{\omega}{t}$$ $$\tau=0.5(10)(0.2)^2\frac{2\pi (50000)}{20\cdot 60}=52.36\ Nm$$

Power:

$$P=T\omega=52.36\frac{2\pi (50000)}{ 60}=274000\ W=274\ kW$$