UNIT 4 OVERVIEW

In Unit 4, we covered 6 major topics:

1. Rotational and Tangential Velocity
2. Rotational Inertia
3. Conservation of Angular Momentum
4. Torque
5. Center of Mass/ Gravity
6. Centripetal/Centrifugal Forces

Rotational and Tangential Velocity

We measure linear motion in speed. For circular motion, however, we have to ways to express velocity:

• Tangential Velocity
• Rotational Velocity

Rotational Speed measures the number of rotations that occur in a certain unit of time.  For instance, A car measures a it's speed in "RPM", or Rotations Per Minute.

Tangential Velocity measures the distance covered per unit of time such as miles per hour (mph) kilometers per hour (km/h).  Therefore, it is still linear speed, but in a circular path.

One thing to remember about tangential velocity is that it depends on RADIAL DISTANCE.  Radial distance is distance from the AXIS OF ROTATION.  They are directly related.  Also, Tangential Speed is also directly related to rotational velocity.  We express both these relationships like so:

v ~ r w

(tangential velocity ~ radial distance * rotational velocity)

-We saw this relationship when we did the activity outside.  We linked arms and created a line, rotating around Maiya as our axis of rotation.  As people moved from closer inside of the circle to the very outside of the circle, they noticed they must walk much faster, even run, to keep the same number of rotations as the people in the inner circle.  

-For instance, the image below shows 4 students on a ferris wheel, Maiya, Catherine, Princess, and Jasmin climbing the bars

Jasmin and Princess will experience the same number of rotations, however, Princess will have to go faster (have a greater tangential speed) to reach them.  This is because her radial distance is greater.

Rotational Inertia
Rotational inertia is a property of an object to RESIST change in spin.
Rotational inertia is similar to inertia, except rather than depending on mass, it depends on DISTRIBUTION OF MASS.

The two dumb-bells shown above have equal weights, however the let's weight is distributed father from the axis of rotation than the right's.  Therefore, it has a larger rotational inertia, and is harder to spin.  The right dumb bell has a smaller rotational inertia, therefore is easier to spin.

Here's a video we created on rotational inertia:

Conservation of Angular Momentum

when calculating angular momentum, we use:

• mv before = mv after

Angular momentum is similar, but now we will use rotational inertia (RI) and rotational velocity (RV).  (these are not the real letters we use, but we will use them now for sake of space)

• RIbefore * RVbefore = RIafter * RVafter

This image shows a spinning ice skater.  We know their momentum before must equal their momentum after (conservation).  As they take their arms in, they are decreasing their rotational inertia, which will increase their rotational velocity.

Torque

Torque is the force that causes rotation.  

Torque = force * lever arm

Lever arm is the distance from the axis of rotation.

This is why we use wrenches of different lengths.  The longer wrenches have a greater lever arm, therefore require less force to unscrew a bolt.

Torque also affects balance which will be explained in the section below...

Center of Mass/ Gravity

The center of gravity for any object is it's average position of all mass

The base of support is the plane on which the object is supported by the ground.

An object will fall if it's center of gravity does not align over it's base of support:

There are two ways you can make something more stable:

1. Create a bigger base of support
2. Lower the center of gravity

This is why wrestlers bend spread their legs (#1) and bend their knees (#2), so they can't be pushed over as easy.

Centripetal and Centrifugal Forces

A centripetal force is a center- seeking force that keeps something moving in a curve:

Why don't you continue forward when your car turns?  Because of Newton's 1st law, your body wants you to.  However, the car door runs into you (centripetal force) and you run into the door (centrifugal force).  When turning, it may feel like you are the one pushing on the door, but this is not a real force.  It is named centrifugal force, however it doesn't really do anything.