Question

A 1.51 kg ball and a 1.97 kg ball are connected by a 1.63 m long rigid, massless rod. The rod is rotating clockwise about its center of mass at 38 rpm. What torque will bring the balls to a halt in 7.5 s? (Give an absolute value of torque.)

Answer 1

Answer:

$T = 1.205\,N\cdot m$

Explanation:

Needed torque can be estimated by means of the Theorem of Angular Momentum Conservation and Impact Theorem. The center of mass of the system is:

$\bar r = \frac{(0\,m)\cdot (1.51\,kg)+(1.63\,kg)\cdot (1.97\,kg)}{1.51\,kg+1.97\,kg}$

$\bar r = 0.923\,m$

Let assume that both masses can be modelled as particles, then:

$[(1.51\,kg)\cdot (0.923\,m)^{2} + (1.97\,kg)\cdot (0.707\,m)^{2}]\cdot (38\,\frac{rev}{min} )\cdot (\frac{2\pi\,rad}{1\,rev} )\cdot (\frac{1\,min}{60\,s} ) -T\cdot (7.5\,s) = 0\,\frac{kg\cdot m^{2}}{s}$

The torque needed to stop the system is:

$T = 1.205\,N\cdot m$