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.

Mass of a Meter Stick -- Torque Lab

Step 1 DEMO:

The meter stick was not balanced on the edge of the table and either fell, or was not actually in a balanced state, meaning that the torques of both sides of the stick were not equal. What is torque? It is the amount of force multiplied by the lever arm that ultimately creates a rotation of the system. The meter stick is the rotation in this lab.

After speculation, (the meter stick balanced at approximately 50cm) we took the meter stick and added a 100gram weight on the end. Once it was steady, the next goal was to balance the stick again, and measure the distance between the weight/(end off the table) and where the axis of rotation was. The lab asked for pictures labeling the center of gravity, the lever arm, and the force.

Step 2 PLAN: 

The equation we used to solve for the meter stick’s mass was derived from the idea that the torque on either side was equal when balanced. Because torque is force times distance, simply put, the new equation was (Fgravity)(distance) = (Fgravity)(distance). Fgravity, we learned in chapter 2, is the same term as weight, which equals (mass)(gravity).

Now: (mass)(gravity)(distance) = (mass)(gravity)(distance)

(0.1kg)(9.8)(30.5cm from table) = (x)(9.8)(19.5 from end of table to 50cm mark)

x = 0.156 kg  OR  156 grams

Percent error: (156 – 150.7) / 150.7 = 3.5% error!!

         

SUMMARY & Explanations – The method that worked…using Mr. Roo as a resource.

*Torque:  what makes an object or system rotate; (force)(lever arm)

*Lever arm:  the distance from the axis of rotation; more distance, easier to rotate

*Force:  a push or a pull on an object; Fgravity is just the weight

*Center of Mass:  where an object’s mass is in relation to the pull of gravity ¯

*Mass:  how much matter an object has

*Weight:  the force of gravity on an object’s mass

Why things are balanced: the torque is equal on either side of a rotating object/system. The bigger the lever arm, the less force is required to rotate the object. The smaller the lever arm, the more force is needed to rotate it. They’re inversely proportional.  

Here are some pictures I made from PowerPoint:

    

   CHEERS.

Torque -- Ch. 8 Resource

We've all been on a see-saw. Well, I hope so. If you haven't, they are fun but dangerous park additions that require 2 people: one on each end. Here's a picture to clear things up.

One person sits on the left end, and another on the right. But if they're masses are not equal, the lever won't be even. The website I found embedded below provides an easy example of torque and how we find it in everyday life. 

Torque = "the product of the rotational force exerted at right angles on the lever, times the distance between the point of force and the fulcrum" (dsc.discovery.com).

• (Torque = force x distance from axis)

http://dsc.discovery.com/tv-shows/mythbusters/about-this-show/physics-of-seesaws.htm

CHEERS.

Angular Momentum -- Ch. 8 Resource

This video is focusing in on how a cat lands on its feet. It is upside-down, then flips over so quickly that it lands on all fours. But how? Look and see--





The cat pulls its legs in towards its body, or axis of rotation. This causes its rotational velocity to increase, allowing for the cat to flip fast enough before landing. However, the cat's rotational inertia is less, so it is easier to [start to] rotate.

Angular momentum = Rotational Inertia x Rotational Velocity.

• RI and RV are inversely proportional: when one increases, the other decreases.

An object has less rotational velocity if the most mass is distributed furthest away from its axis of rotation. It also has more rotational inertia because it is harder to start/stop/continue spinning.

An object has more rotational velocity if the most mass is distributed closest to its axis of rotation. It also has less rotational inertia because it is easier to start/stop/continue spinning.

Hope you enjoyed,

CHEERS.