Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 32, 33, 34 Hw: Chapter 14 problems and exercises

Kinematics

Vector directed along velocity The larger the momentum, the larger force you need to apply in order to change its magnitude or direction Motion along the straight line: momentum

Rotational motion: angular momentum Moment of inertia Angular velocity Vector along axis of rotation

Conservation of angular momentum: when radius decreases, rotation velocity goes up

Torque and Angular Momentum Conservation of Angular Momentum

Moment of Inertia For symmetrical objects rotating about their axis of symmetry:

Two men of equal mass are skating in a circle on a perfectly frictionless pond. They are each holding onto a rope of length R. What happens to the magnitude of momentum of each man if they both pull on the rope, “hand over hand”, and shorten the distance between them to R/2. (Assume the men again move in a circle and the magnitude of their momenta are equal).

Problem 6 p.267 Consider a massless teeter-totter of length R, pivoted about its center. One kid of mass m 2 sits on the right end and another of mass m 1 sits on the left end. What is as a function of θ, the angle the board makes with horizontal?

Pr. 1 A bullet of mass m is fired in the negative x direction with velocity of magnitude V 0, starting at x = x 0, y=b. (y remains constant) What is its angular momentum, with respect to the origin, as a function of x? Neglect gravity. Pr. 2 A ball of mass m is dropped from rest from the point x = B, y=H. Find the torque produced by gravity about the origin as a function of time.

An ant of mass m is standing at the center of a massless rod of length l. The rod is pivoted at one end so that it can rotate in a horizontal plane. The ant and the rod are given an initial angular velocity  0. If the ant crawls out towards the end of the rod so that his distance from the pivot is given by, find the angular velocity of the rod as a function of time, angular momentum, force exerted on the bug by the rod, torque about the origin.

Newton’s law of gravitation

Orbital motion Conservation of Angular Momentum

A man stands on a platform which is free to rotate on frictionless bearings. He has his arms extended with a huge mass m in each hand. If he is set into rotation with angular velocity  0 and then drops his hands to his sides, what happens to his angular velocity? (Assume that the man’s mass is negligible and that his arms have length R when extended and are R/4 from the center of his body when at his sides.)

Have a great day! Hw: Chapter 14 problems and exercises