Atwood Machine

The Atwood machine was invented in 1784 by, yes Mr. Atwood. Two weights of mass and are connected by a string over a pulley. The acceleration is

Here is a demonstration from MIT, USA:

Homework: check that the experiment measures an acceleration as given by the equation above.

Circular motion

When an object moves in a circular orbit (of radius ), the acceleration has two components, tangential and radial. The angular speed is defined as , and angular acceleration defined as ( is the angle that measures the movement of the position vector); the two components are then generally:

In many cases we work with uniform circular motion, in this case .

credit: Prof. Walter Lewin of MIT (course 8.01, Physics I: Classical Mechanics, fall 1999).

Topics covered in this lecture:

Circular Motion – Centrifuges Moving – Reference Frames – Perceived Gravity

How to solve it

George Polya (1887-1985) was a Hungarian mathematician. He is famous for work on mathematics education, and for the 4 steps to solve a problem:

1. understand the problem

2. devise a plan

3. carry out the plan

4. look back

We can use this method to solve physics problems also. Try it! (It is a good idea to make a drawing of the situation in step 1). Single page explaining Polya’s principles:

how-to [PDF]

Video lectures: 3D Kinematics, projectile motion

credit: Prof. Walter Lewin of MIT (course 8.01, Physics I: Classical Mechanics, fall 1999).

Topics covered in this lecture:

Vectors — dot product — cross product — kinematics — projectile motion

(Young and Freedman, chap. 3)

Interactive simulation: Projectile motion

Projectile motion: footballs, humans and pianos – they all (ideally) move in the same way. Try the interactive simulation by following this link. The equation of motion is just

[the simulation is from University of Colorado at Boulder].