A particle has a mass of 10 kg and a velocity of 5 m/s. What is the momentum of the particle? (Answer: 50 kg·m/s)

An impulse of 20 kg·m/s acts on the particle in problem # 1, in the same direction as the velocity. What is the final velocity of the particle? (Answer: 7 m/s)

If the impulse in problem # 2 is delivered for a duration of 0.5 seconds, what is the average force acting on the particle? (Answer: 40 N)

An elastic collision occurs in one dimension, in which a 10 kg block traveling at 5 m/s collides with a 5 kg block traveling at 3 m/s in the same direction. What are the velocities of the two blocks immediately after the collision? (Answer: 3.67 m/s, 5.67 m/s)

An inelastic collision occurs in one dimension, in which a 10 kg block traveling at 5 m/s collides with a 5 kg block traveling at 3 m/s in the same direction, and they stick together. What are the velocities of the blocks immediately after the collision? (Answer: 4.33 m/s)

A simple and practical understanding of conservation of momentum problems is given by the following: When a figure skater makes a jump, he increases his rotation speed by pulling together his arms and legs. This reduces his rotational inertia causing him to spin faster. If the initial spin rate of a figure skater is 1 RPM and he decreases his rotational inertia by half during the spin, what is his final spin rate? (Answer: 2 RPM)

When two billiard balls collide the collision is assumed to be elastic. Show that for a general case, where the collision is not head on, the cue ball moves in a direction perpendicular to the direction of the object ball, after impact. Assume that the balls have the same mass and the object ball is initially at rest.

(For the answer see the physics of billiards page)

A solid ball of mass

Assume that the ball pivots about the tip of the bump during, and after impact.

(For the answer see the impulse and momentum page)

In the angular momentum page we showed how the angular momentum equations for a rigid body are derived. The figure below shows the set up used for the derivation.

Where:

Introduce the following new variables:

The following vector equation defines the angular momentum (

If we set,

and

show that the angular momentum (

where

See the problem, Cat righting reflex. This is an excellent real-world example to aid your understanding of conservation of momentum problems.

1.

2.

3.

I created a physics analysis for these three problems, in PDF format. It's available through this link.

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