An oversized yo-yo is made from two identical solid disks each of mass M=2.00kg

Question

An oversized yo-yo is made from two identical solid disks each of mass M=2.00kg and radius R=10.0cm. The two disks are joined by a solid cylinder of radius r=4.00cm and mass m=1.00kg. The the center of the cylinder as the axis of the system, with positive torques directed to the left along this axis. All torques and angular variables are to be calculated around this axis. Light string is wrapped around the cylinder, and the system is then allowed to drop from rest.

What is the moment of inertia and torque of the system?

Explanation / Answer

Torque: T=F*r. Where F be tension of the string. Moment of inertia. 0.5*(M*R^2*2+m*r^2)=0.0208(kgm2). let w be the angular acceleration rate and a be the linear acceleration rate (downward). w=T/I a=((2M+m)*g-F)/(2M+m). and a=w*r. so T*r/I=a=F*r^2/I=0.077F a=(49-F)/5=9.8-F/5. so 9.8=(0.077+0.2)*F so F=35.4(N). so T=F*r=1.4(Nm)

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