Unit 4 Reflection

Rotational and Tangential Velocity
Rotational Velocity:  

• number of complete rotations, revolutions, cycles, or turns per time unit
• same= with merry-go-rounds, train wheels, etc
• know something has the same rotational velocity when connected by a shaft

Tangential velocity:

• same= with gears, belts, etc
• different=  tapered train wheels
• know something has same tangential velocity when covers same amount of distance in the same amount of time.

The further away from the axis of rotation, the more tangential velocity something has.

Train Problem

We know that the wheels have the same rotational velocity because they are connected by a shaft, making them rotate with the same velocity. We know that the larger-inner parts of the wheels have a greater tangential velocity than the smaller-outer parts because they cover more distance in the same amount of time. This makes the wheels self correct because if the wheels start to get off track, the larger-inner parts will go faster, making the trains "correct" again.

Inertia
 Why does a Frisbee roll faster than a hula-hoop down a hill?

The Frisbee will go faster than the hoop because the distribution of mass is closer to its axis of rotation, causing the Frisbee to have less rotational inertia and the hoop.

Mass close to the axis of rotation= less rotational inertia
Mass away from the axis of rotation=more rotational inertia

Conservation of Angular Momentum
Rotational Inertia X Rotational Velocity = Angular/Rotational Momentum

Takes distribution of mass into account

Angular P before= Angular P after
(Rotational Inertia X Rotational Velocity) BEFORE = (Angular/Rotational Momentum) AFTER

The distribution of mass changing causes the Rotational inertia to change, which causes the Rotational velocity to change.

           

Torque
3 Ways to Cause a Larger Torque:

1. Larger lever arm
2. Large Force
3. Both

DISCLAIMER!!!!!!------- Torque is NOT a FORCE

The lower the center of gravity, and the wider the base of support, the more stable something will be

Center of Mass/Gravity

STEP 1:

This picture depicts an unbalanced meter-stick with a torque. It is unbalanced because the center of gravity is not supported. The force comes out of the center of gravity, causing it to tilt counter-clockwise. The lever arm is the distance from the Center of Gravity to the base of support. A Torque=(Force)(Lever Arm)

Step 2: 

This picture depicts a balanced meter-stick. It is balanced because the Center of Gravity is supported. The force comes out of the Center of Gravity, and since it is within the support, the meter-stick will not tilt or topple over. There is no lever arm because the meter-stick is balancing on its Center of Gravity.

Step 3:

A 100g weight was added to the meter-stick, which changed the system's center of gravity, but not the Center of Gravity of the meter-stick itself. On lever arm is from the edge to the base of support, and the other is from the base of support to the meter-stick's center of gravity. Since the Lever arm from the weight to the base of support is longer than the other one, to make the two Torques equal, which has to happen for something to be balanced, there needs to be a greater force on the side with the shorter lever arm. That makes the equation (Force(a))X(Lever Arm(a))=(Force(b))X(Lever Arm(b)) true.

Part 3:

Torque=Force X Lever Arm

We found the Center of Gravity of the meter-stick by itself, which was 50.25 cm. When we added the 100g weight, the lever arm with the weight is 29.5 cm, and the other lever arm is 20.75 cm. w=mg, which means w=0.1Kg*9.8-- Weight=0.98N Since I know the lever arm and the force of one side of the meter-stick, I can find the Torque. Torque=(0.1X9.8)(29.5)--- Torque=28.9 N cm. This is the Torque for both sides because for something to be ballanced, the clockwise Torque= the counter-clockwise Torque. This means that 28.91=20.75(F)--- 1.39=Force. w=mg---- 1.39=m(9.8)---1.39/9.8=0.1418 which, when converted from Kg to g, you get 141.8g. When we weighed our meter-stick, the weight was 142.9g.

Centripetal/Centrifugal Force
Why, when rounding a curve, you lean up against the door:

I am going straight, and want to keep going straight because of Newton's first law. Because of this, I have inertia and keep wanting to go straight. The car door pushes me inward, and I push the car door outward.

Centripetal Force: Center-seeking force
Centrifugal Force: Fictitious Force-- Center-fleeing force