Unit 4 Summary

I. ROTATIONAL AND TANGENTIAL VELOCITY

Tangential velocity is the speed at which an object travels along a circular path

àdepends on the object’s distance from the axis

Rotational velocity is the number of revolutions that an object makes per unit of time (RPM’s)

Tangential velocity is directly proportional to rotational speed and radial distance

So say hypothetically, you put a raisin on the outside of a record, and one closer to the middle of the record...which has the greater a. rotational velocity, and b. tangential velocity

A. The raisin on the outside has to travel faster in order to cover a larger distance than the one on the inside. They will have the same number of revolutions per minute, therefore the same rotational velocity

B. We already established that the raisin on the outside must go faster because it is traveling a longer distance in order to keep up with the raisin on the inside. Therefore, the outside raisin has the greater tangential velocity.

How do train wheels work?

Train wheels are narrow on the outside, and wide on the inside. They will have the same rotational speed (RPM’s), but different tangential speeds. This is because the wider inside has to move faster too keep up with the narrow inside, so that they will have to same RPM’s. When the wide part is resting on one of the tracks, it has a faster speed that causes the train to curve towards the middle of the track, and self correct.

II. ROTATIONAL INERTIA AND ANGULAR MOMENTUM

Watch this video to better understand rotational inertia! I would definitely click that link if I were you…

To recap, a golf ball (solid) will have less rotational inertia than a ping-pong ball (hollow). This is because the mass of the golf ball is closer to its axis of rotation

Angular momentum= rotational inertia x rotational velocity

It is also important to remember that momentum can neither be created nor destroyed

total (angular) momentum before= total (angular) momentum after

III. TORQUES AND CENTER OF MASS/GRAVITY

A torque, in essence, is a factor that causes an object to rotate. In order for a torque to be present, you must have a force and a lever arm.

àLever arm- distance from the axis of rotation to force

    Torque= force x lever arm

The center of mass is the average position of all combined masses in an object. 

àa lever arm can occur if the center of gravity is NOT above the base of support

If you are trying to make something rotate, the best way to do so is to make the lever arm larger. Similarly, if you don’t want rotation, shorten the lever arm.

When something is balanced…

The torques are equal, but forces/lever arms are different

Clockwise torque = counter clockwise torque

F x lever arm= f x lever arm

IV. CENTRIPETAL AND CENTRIFUGAL FORCES

Centripetal force is a center seeking force that causes an object to follow a curved path.

àWhen you are riding in a car and you take a sharp curve, the centripetal force causes the car to curve inwards. Due to inertia, your body will stay in the same place while the car itself turns. Essentially, the side of the car moves into you while you sit still causing you to hit the car door. This phenomenon, that you are hitting the side of your car, is called centrifugal force. However, it is just a term used to describe this experience, it is not an actual force. Be weary…

If you have ever seen a racecar track, you will notice that the track itself has an elevated slant. This can be explained with centripetal force, check out the diagram below.

Here is another example using the flying pig from class