Answer:
[tex]T = 1.205\,N\cdot m[/tex]
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:
[tex]\bar r = \frac{(0\,m)\cdot (1.51\,kg)+(1.63\,kg)\cdot (1.97\,kg)}{1.51\,kg+1.97\,kg}[/tex]
[tex]\bar r = 0.923\,m[/tex]
Let assume that both masses can be modelled as particles, then:
[tex][(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}[/tex]
The torque needed to stop the system is:
[tex]T = 1.205\,N\cdot m[/tex]
