Angular Momentum and its Conservation

The total angular momentum of a rotating body remains constant if the net torque acting on it is zero.

Object rotating on a String of Changing Length

A mass m attached to the end of a string revolves in a circle on a frictionless tabletop. The other end of the string passes through a hole in the table. Initially, the mass revolves with a speed v1 = 2.4 m/s in a circle of radius r1 = 0.80 m. What is the speed, v2, of the mass when the radius is 0.40 m?

1. Why is it possible for a high diver to execute more front somersaults in the tuck position that in the layout position?

2. Why do figure skaters spin faster when they pull in their arms?

1. If you look down the inside of barrel of a rifle, you see long spiral grooves. When the bullet travels down the barrel, these grooves cause the bullet to spin. Why would we want the bullet to spin?

2. Bicycle wheels are normally about 2 feet in diameter. Imagine that a bicycle was constructed with 4-inch-diameter wheels but was otherwise the same size as a normal bicycle. How would the small wheels affect the bicycle’s stability?

Classical Relativity

A Reference System

Reference system : the set of objects that are not moving relative to each other and that can be therefore used as the basis for detecting and describing motion.

Motion Viewed in Different Reference System

Galileo asked if observers could decide whose description was “correct”. He concluded that they couldn’t. In fact, each observer’s description was correct!

We define an inertial reference system as one in which first Newton’s law is valid.

Galilean Principle of Relativity

The laws of physics are the same for all inertial reference systems.

Comparing Velocities

Comparing Energies

Accelerating Reference System

Forces that arise in accelerating reference systems are called inertial forces.

Another common label for these forces is fictitious forces.

Realistic Inertial Forces

Questions

1. Alice in Wonderland begins with Alice falling down a deep, deep rabbit hole. As she falls, she notices that the hole is lined with shelves and grabs a jar of orange marmalade. She is afraid to drop the jar for it might hit somebody on the head. What would really happen to the jar if Alice had dropped it? Describe its motion from Alice’s reference system and from the reference system of someone sitting on the shelf.

2. Imagine riding in a class-walled elevator that goes up the outside of a tall building at a constant speed of 20 m/s. As you pass a window washer, he throws a ball upward at a speed of 20 m/s. Assume that you drop a ball out of window at the same instant. Describe the motion of each ball from the point of view of window washer and your point of view.

3. You wake up in a windowless room on a train, which rides along particularly smooth tracks. Imagine that you have a collection of objects and measuring devices in your room. What experiment could you do to determine whether the train is stopped at the train station or moving horizontally at a constant velocity?

Assume that you are riding in a windowless train on perfectly smooth tracks. Imagine that you have a collection of objects and measuring devices in the train. What experiment could you do to determine whether the train is moving horizontally at a constant velocity or is speeding up?