Unit 4 Blog Reflection -- Jan.

Part A.) WHAT WE LEARNED

1.) Circular Motion (tan/rot Velocity); Gears; Train
2.) Rotation Inertia & Angular Momentum; Hoop/Ball
3.) Conservation of Momentum; Skater; RI versus RV
4.) Torque
5.) Center of Mass & Center of Gravity; Sports
6.) Centripetal Force (and centrifugal)
7.) Extra Problems to Consider


A1.) Circular Motion (tan/rot Velocity)

Linear Speed is exactly the same as Tangential Speed. The equation in words is "the direction of motion is tangent to the circumference of the circle or rotational axis per time interval."

• Formula: distance/time

Rotational Velocity is completely different. It is the amount of rotations an object or system makes in a certain time interval.

• Formula: rotations/time

Two things can have the same tangential velocity but different rotational velocities.  Two gears may cover the same distance over a period of time, but they don't have the same # of rotations.
A smaller gear would have to rotate maybe twice as many times as the big gear rotates to cover the same tangential distance.

Similarly, train wheels keep a train on the tracks --> The wheels are slanted with the bigger (larger radius) side on the inside of the track, while the smaller side is on the outside. This makes the larger side have a higher tangential velocity because it has to cover more distance to catch up.
The wheels will tend to rotate towards the middle of the track; the larger side covers more distance per revolution and it turns. They re-align and on turns, the train can straighten-up.


A2.) Rotation Inertia & Angular Momentum; Hoop/Ball

Rotational Inertia is a branch of inertia that states an object will resist change in rotation, whether it be to start or stop the rotation.
What determines how much inertia an object has is the distribution (position) of its mass. When more of the mass is further away from the axis of rotation, there is more inertia; it will be harder to start/stop its spin. When the mass is closest to the axis of rotation, the object will be easier to start/stop its spin.

The hoop and ball: Explained here in this podcast video, a hoop and a solid cylinder race down a ramp. Both have the same mass and radius. Why does the hoop lose? Look below!


 
Angular Momentum is the rotational inertia multiplied by the rotational velocity of an object. These terms are inversely proportional, so as one gets big, the other gets smaller. Vice-versa.

• Formula: RI x RV

A3.) Conservation of Momentum

The conservation of momentum occurs when an object is rotating, such as a ice-skater. Let's say that she has her arms out, and suddenly pulls them in toward her body. What happens?
At first, her arms are far from her axis of rotation, so she had a high rotational inertia and a low rotational velocity (formula).
But as her arms go in, she spins faster! Her rotational inertia is low and so her rotational velocity must get higher to compensate for the change. As one goes up --> the other goes down.

In this picture, the "I" stands for rotational inertia. The "w" stands for rotational velocity.

BOTH girls in the picture has the same angular momentum because RI x rv = ri x RV.

A4.) Torque 

Torque is a force that causes rotation. 

• Formula: force x lever arm

A force is a push or a pull on an object.

A lever arm is just the distance between the force-action and the axis of rotation. The lever arm is perpendicular to the force.

So as the formulas shows us, the force and the lever arm are directly proportional. Whichever gets larger helps raise the torque and cause a rotation of some sort.

Let's do a torque problem: There's a 2N ball and a ball that is 3N resting on a balance with a fulcrum in the center. The 3N ball is 4 meters from the axis of rotation. How many meters (how long is the lever arm) is the 2N ball from the center?

clockwise torque = counterclockwise torque
(force)(lever arm) = (force)(lever arm)
(3N)(4m) = (2N)(x)
x = 6 meters


A5.) Center of Mass & Center of Gravity; Sports

Center of Mass: the point where the average distribution of mass is located on an object (the middle usually).

Center of Gravity: the point where gravity is pulling down an an object.

Base of Support: the foundation on which an object is located, right above the support force.

Why are football players less likely to be pushed over when they keep their legs should-width vs. feet together? 
~ With legs further apart, the base of support is widened, giving a larger foundation for the object. It is harder for the center of gravity to go beyond the base of support. When it does go over, however, the object will fall.

Why are wresters told to bend their knees when wrestling?
~ They bend their knees so that their center of mass is lower to the ground (and base of support), so it is harder to get the center of mass beyond the base support and it would be unlikely for the wrester to fall over sideways.


A6.) Centripetal Force (and centrifugal)

Centripetal Force: center-seeking force (toward the axis of rotation).

Centrifugal Force: center-fleeing force; it is FICTICIOUS (away from the axis of rotation).

This image is of a ball rotating in a circle. The centripetal, centrifugal (fictitious), path of inertia (tangent line), and center are all labeled.

A7.) Extra Problems to Consider

• Bus problem: you hit person next to you as the bus turns a sharp left...why?
• Satellite: is the satellite stationary above earth? How do the forces/vector quantities keep it in orbit?
• Why does water fly out of a washing machine? Is the water moving on a curved or straight-line path?
• Why are racetracks banked with one edge higher than the other? Where is the centripetal force acting on it? Add vectors to prove your answer.

Part B.) REFLECTION AND CONNECTIONS

What I've found difficult about this unit is the last topic we studied: centripetal force. I understand the problems and have contributed in class, but I needed more time to study it.

I overcame this difficulty by using my quizzes and notes to re-write the answer and descriptions of each term and each problem we did together. It helped be see physics not just on paper, but also in my head.

My effort in this class has been right on target. I do my homework and participate every day, because the material is interesting and my classmates help each other. The formula/problem-solving questions are fine for me; I do each step carefully and end up with the right answer (unless I did math wrong or didn't have persistence!)

My goal for the next unit is to be better organized with my quizzes and other scattered papers. Right now, I have everything in my spiral notebook and the inside cover of my binder. Also, I want to start doing more things with other people in my class, that I don't typically talk to every day. I am excited for the next chapter!

~ Connections

• My desk dresser is a small, rolling 2-drawer cabinet. All my of my school-supplies is in there, and when I open the drawer, the dresser falls over! I recognized that its center of mass had been shifted, and was beyond the base of support. 
• Just like an ice-skater, I rollerblade. Whenever I spin in circles with my arms spread out, I slow down, but when they are tucked in, I spin faster!
• Lastly, I was opening my dorm room door. My hand acted as the twisting force, and my fingers the lever arm. The door knob turned and my door opened. I actually noticed the door-stop as well.

CHEERS.