As an object rises and falls this is the graph of the energy compared to height and time.

. . .

No longer can we think of objects as dots.

Torque! Right Hand Rule: Put the fingers of your right hand in the direction of r (the green arrow). Curl your fingers in the direction of the force (the red arrow). The direction your right thumb points is the direction of the torque vector (the blue arrow). Torque causes objects (or systems in general) to rotate.

CHeck out that torque.

It’s all cross products and dot products from now on my little babies.

Torque (cross products) vs. Work (dot products)

Torque!

Well, this is confusing. Work and torque have the same units, but mean entirely different things. That’s why many use the units of Joules for work and Nm for torque. A joule and a Nm are the same thing mathematically, but they are different conceptually.

A vector into the board vs. a vector out of the board.

If it is a two dimensional object, there is no way you can represent the torque vector in that plane because you can not represent circular motion with a straight vector. (Vector’s can’t be curved. So . . . we have to put the vector in the third axis.

7.8.2

7.8.2b

You can use torque to determine the weight of a meterstick. Gravity acts as if all the mass of the stick is at the Natural Balance Point (NBP). As far as gravity is concerned, there is no stick.

7.8.3

7.8.5

7.9.2

7.9.3

7.9.4

7.9.6

7.9.7a

7.9.7b

Every equation in circular world has a corresponding equation in linear world.

From 7.10.4 (the drawing is off).

Vectors are the lowest form of a tensor. Tensors are solved using Matricies.