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I am having a heck of a time with collisions in 2D and with rotational kinetics and rotational dynamics. I have posted 5 questions below that I seem to be having the most troubles with. I know it my be alot to ask but if anyone here can help me to understand how they got to the answers I would be forever greatful, and will pay it forward.

Thanks

1. A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball as shown. If the first ball moves away with angle 30° to the original path, determine

- the speed of the first ball after the collision.

- the speed and direction of the second ball after the collision.

2. A light string is wrapped around a solid cylinder and a 300 g mass hangs from the free end of the string, as shown. When released, the mass falls a distance 54 cm in 3.0 s.

- Calculate the mass of the cylinder.

3. A solid sphere of mass 6.0 kg is mounted on a vertical axis and can rotate freely without friction. A massless cord is wrapped around the middle of the sphere and passes over a 1.0 kg pulley and is attached to block of mass 4.0 kg, as shown. What is the speed of the block after it has fallen 80 cm? Treat the pulley as solid cylinder.

4. Consider a uniform rod of mass 12 kg and length l.0 m. At its end, the rod is attached to a fixed, friction-free pivot. Initially the rod is balanced vertically above the pivot and begins to fall (from rest) as shown in the diagram. Determine,

the angular acceleration of the rod as it passes through the horizontal at B.

the angular speed of the rod as it passes through the vertical at C.

5. A uniform vertical beam of mass 40 kg is acted on by a horizontal force of 520 N at its top and is held, in the vertical position, by a cable as shown.

Calculate the tension in the cable?

Determine the reaction forces acting on the beam by the ground?

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