Answer to Question #157281 in Mechanics | Relativity for Tinotenda

Question

A light arm 500m long, pivoted at its center, carries a 10kg mass at each end. If a couple of 3Nm is applied to the arm, calculate the angular acceleration produced.

Answer 1

Explanations & Calculations

• The moment of inertia of the arm can be neglected since it is light in weight and the moment of inertia of the system created by the two masses can be evaluated by considering each mass individually.
• That of a single mass is $\small I=mr^2=10kg\times (250m)^2=2500kgm^2$
• Then that of the entire system is $\small I_{sys}=2I=5000kgm^2$
• Then upon the given torque, the angular acceleration it gains can be calculated by the formula,

$\qquad\qquad \begin{aligned} \small \tau_{net}&= \small I_{sys}\alpha\\ \small 3Nm&= \small 5000kgm^2\times \alpha\\ \small \alpha&= \small \bold{0.0006 \,rads^{-2}} \end{aligned}$

• With that enormous arm length, such a small angular acceleration is possible.