Instructor: Dr. Tatiana Erukhimova Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 38, 39, 40 Hw: Chapter 15 problems and exercises

For symmetrical objects rotating about their axis of symmetry: Second Law:

The rope is assumed not to slip as the pulley turns The rope is assumed not to slip as the pulley turns. Given m1, m2, R, and I find the acceleration of mass m1. I m1 m2 R

Two masses, and , are attached by a massless, unstretchable string which passes over a pulley with radius R and moment of inertia about its axis I. The horizontal surface is frictionless. The rope is assumed NOT to slip as the pulley turns. Find the acceleration of mass .

A solid sphere rolls down an inclined plane of angle θ without slipping. a) Find the acceleration of the sphere. b) Find the maximum θ if the coefficient of static friction is μ.

Gyroscopic precession The precession of a gyroscope shows up in many “common” situations.

A rotating flywheel

Conservation of Momentum If the collision is perfectly elastic, the kinetic energy is conserved!

Circular Motion y x

Torque and Angular Momentum Conservation of Angular Momentum

Test 3 results Average 65.6 Median 69.5 30 23 20 16 15 10 7 >90 >80 >70 >60 >50 >40 <40

Ch. 17 Statics

Ch. 17 Statics Parallel-Axis Theorem A rigid body has a lower moment of inertia about an axis through its center of mass than about any other parallel axis

There is a ladder against a wall There is a ladder against a wall. There is no friction at the wall and the coefficient of friction at the floor is . At what angle can the ladder be placed so that it would slip if the angle were decreased infinitesimally?

The advantage of a lever GIVE ME A PLACE TO STAND AND I WILL MOVE THE EARTH                                                  

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