Instructor: Dr. Tatiana Erukhimova Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 31, 32, 33

Polar coordinates

A ball of mass m is swung around a circle at the end of a string of length L. The string will break if the tension in it exceeds a critical value, Tc. What is the largest constant angular velocity the ball can have without breaking the string?

A ball of mass m is swung around a circle at the end of a string of length L. What is the minimum  the ball can have and still travel in a circle without string becoming slack?

A plane is flying in an arc at the speed of v0 A plane is flying in an arc at the speed of v0. At the top of arc the passengers experience a sense of weightlessness. What is the radius of the arc?

Rotational Motion Whirling Beaker of Water

A 3000 kg spacecraft is in a circular orbit 2000 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4000 km above the surface?

A race track designer wants to have the cars able to maintain a speed vmax without skidding on a circular track. If the track is flat with a coefficient of friction  what does the radius have to be?

Platform rotates with angular acceleration (t)=t Platform rotates with angular acceleration (t)=t. A man starts a distance L from the center and walks in along a straight line painted on the platform towards the center. He decreases his distance from the center as a constant rate, vc. What force does the platform exert on the man, as a function of his distance from the center?

Newton’s Laws 1st Law: A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration 2nd Law: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. 3rd Law: For every action there is an equal, but opposite reaction

Conical pendulum

A frictionless track contains a circular section of radius R as shown A frictionless track contains a circular section of radius R as shown. What is the minimum height at which a block must be started in order for it to go around the loop without falling off the track? H R

Kinematics

Have a great day! Reading: Chapter 12 Hw: All Chapters 12, 13 problems and exercises