Motions

Kinematics

variables

Dynamics

F=ma - Torque moment of inertia

Energy

Momentum

Rotational Kinetic Energy

Angular momentum

Kinematics

Angular terms

Degrees, revolutions

RPM

The blades of a blender rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?

How they are related

This L is arc length, think of it as part of the circumference

note it is in meters.

The velocity is a tangential one

Similarly the acceleration,

note it is only true if

non-uniform circular motion

arc

v

tan

Note that all angular

terms are defined as

positive in a CCW

and negative in CW

One final note, Rolling

This is just

Translational motion

This is just

Rotational Motion

Added together

Rolling motion

Note, no slipping on contact

Thus: velocity of Center of Mass is

equal to velocity tangential

Torque

Think of opening this door.

What makes it easier, or harder

Or maybe more effective

What quantities does it depend on.

This is in essence the following

F

r

r

Because of this we need to change our definition of Newton's

2nd law, and thus redefine rotational dynamics.

Use Torque, at a 90 degree angle.

As well, use the definition of angular acceleration.

Here we make the comparison and define

the moment of inertia

3 Things

Angle

Force

Distance

Moment of Inertia

The more mass at a larger radius the bigger the moment of inertia is.

This is analogous to linear inertia, or just simply mass.

It is still the term that describes the resistance of force to motion

The difference is the moment of inertia is dependent upon the radius of what is being rotated.

The actual practice of adding up all of these

masses at all distances is a bit tricky

most texts have nice table of some common shapes

here is one such table

only use this with point masses

**Energy**

**At the bottom of a hill, to be the fastest rolling object it must have the ______ moment of inertia.**

A. Largest

B. Smallest

A. Largest

B. Smallest

**While spinning if an individual**

extends their arms

their moment of interia:

A. increases

B. decreases

Remains the same

extends their arms

their moment of interia:

A. increases

B. decreases

Remains the same

Linear

Rotational

Momentum

Conservation

**Note, in angular momentum, the**

moment of inertia can change.

moment of inertia can change.

**If I were spinning with a weight at an initial angular velocity and then simply let go of the weight, would my angular velocity:**

A Increase

B Decrease

C Remain the same?

A Increase

B Decrease

C Remain the same?

**torque Demo**

Demo

**Demo**

" I need some help wrapping my mind around using radians rather than degrees. Can you explain that more please?"

"I still do not understand torque very well."

" Can you go torque and forces that act to tilt the axis? I am also unclear how torque and rotational inertia work together/correlate... "

"Are we going to be solving problems in this chapter using multiple laws every time? (Newtons, Keplers, Dynamics...)"

"The homework problem the last one i am having trouble setting it up"

momentum

rods

turn table

**demo**