Two masses —m1 and m2— are connected by light cables to the perimeters of two cylinders of radii r1 and r2 respectively, as shown in the diagram. The cylinders are rigidly connected to each other on a common axle. The moment of inertia of the pair of cylinders is =45 kgm^2. Also, r1= 0.5 m, r2 = 1.5 m, and m1 = 20 kg. Note: m1 is hanging from the small cylinder, and m2 is hanging from the large cylinder. Determine m2 such that the system will remain in equilibrium. The mass m2 is removed and the system is released from. Determine the angular acceleration of the cylinders. Determine the tension in the cable supporting m1. Determine the linear speed of m1 at the time it has descended 1 m.

Part a)

Mass of m2 is given as

Part b)

Angular acceleration is given as

Part c)

Tension in the rope is given as

Explanation:

Part a)

When m1 and m2 both connected to the cylinder then the system is at rest

so we can use torque balance here

Part b)

When block m_2 is removed then system becomes unstable

so force equation of mass m1

also we have

now we have

so angular acceleration is given as

Part c)

Tension in the rope is given as

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.

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