Rotational and Tangential Velocity:
When speaking about rotation, there are two different kinds of velocity. There is rotational(or angular) velocity, and tangential(or linear) velocity.
Rotational velocity: measures how many times something rotates in a given unit of time.
Tangential velocity: measures distance over in a given unit of time. This is the kind of velocity we were already familiar with.
There are many situations where these two seem similar but are different. For instance when two children are riding on a merry go round, one on the outermost horse, and one on the inner most horse, their rotational speed is the same. If you can imagine, they rotate the same number of times per minute. However, the outermost child must cover more distance and therefore has a higher tangential velocity.
Rotational Inertia:
Regular Inertia represents something's resistance to change.
Rotational Inertia: Rotational Inertia is specifically an objects resistance to change rotation.
Inertia in regular circumstances is usually represented as mass. With rotational inertia it refers specifically to the distribution of the mass. When the mass is distributed further from the axis of symmetry, the rotational inertia increases. Be careful to not mistake this for increased rotational velocity. Inertia is resistance, so when the inertia increases, the rotational velocity decreases. The converse is true for when the inertia decreases.
An Example of this is when an ice skater spins. When the ice skate pulls their arms(mass) in closer to their axis of symmetry, their rotational velocity increases. And when they extend their arms, they slow down.
Conservation of Angular Momentum:
We know very well that momentum is conserved. That is total momentum before = total momentum after.
The switch to angular momentum is ridiculously simple: angular momentum before = angular momentum after.
And Rotational Momentum is also similar to normal momentum:
Angular Momentum = (Rotational velocity x (Rotational Inertia)
This principle of conservation simply states that, for example the ice skater, would have the same angular momentum when she pulled her arms in as when she extended them out. This is because of the way inertia and velocity act opposite to each other. When inertia increases, velocity decreases and vise versa. They are always balancing each other out.
Torque:
Torque is the thing that causes the rotation.
Torque is made up of two components: Force and Lever arm.
Torque = Force x Lever Arm
For instance in this picture, the side of the see saw with the girl on it has a greater Torque because she has a greater force, so it rotates with a counterclockwise torque.
Each rotation has a clockwise torque and a counterclockwise torque.
When something is balanced, the two torques are equal. That is,
Clockwise Torque = Counter Clockwise Torque
Here is an example of a meter stick that has been balanced on the edge of a table with a 100 gram weight on one side and the calculations to prove it is balanced:
*Remember that the Force is the Center of Gravity. The Lever Arm is the distance from the Center of Gravity to the axis of rotation.
Center of Mass/Gravity:
To keep balanced you must keep your Center of Gravity over your base of support.
For instance, The leaning tower of Pisa is tilted, however, it's Center of Gravity is still over it's base of support.
This is why football players keep their feet further apart, because widening your base of support makes it easier to keep your Center of Gravity over it. And they are less likely to fall over.
When wrestlers bend their knees, they do so to lower their center of gravity closer so that is, again, harder to get it out of the base of support, and thus harder to knock them over.
Centripetal Force:
Centripetal Force is a force that goes inwards from an object to the center as it rotates.
This is why it is also called a center seeking force.
It is a combination of an object that is already moving forward and the force of gravity downwards.
Here is a picture of centripetal force:
(ps. sorry this is the lamest diagram ever...but it was either super simple or super complicated. If you need visual help check out the podcasts.)
Remember that centrifugal force is not real!
And that was Unit 4!
No comments:
Post a Comment