Question

A 20 kg object is hangs at the end of a 3.0 m horizontal rod of mass 5.0 kg that is hinged to a pole as shown in figure below. To support the hanging object, a cable is tied at an angle 55⁰ at the middle of the rod. If the cable breaks, find the magnitude and direction of angular acceleration of this system.

Answer 1

Calculation

• Using $\small \tau= I \alpha$, you can calculate the angular acceleration

$\qquad\qquad \begin{aligned} \small \Sigma Fd&=\small \Sigma mr^2\times\alpha\\ \small (20g\times3m)+(5g\times\frac{3}{2}m)&=\small[20kg\times(3m)^2+5kg\times(1.5m)^2]\times\alpha_{initial}\cdots[g = 9.8]\\ \small a_{initial}&=\small \frac{661.5\,Nm}{191.3\,kgm^2}\\ &=\small \bold{3.5\,rads^{-2}} \end{aligned}$

• Direction is perpendicular to the plane in which the rotation takes place.