In this photo the simple pulley system makes it much easier to pull the american flag up the flag pole. Since the distance of the rope is very large, it takes a very small amount of force to pull the flag up and down the flag pole. So the work you do is equal to a large distance and a small force (work=Df).
This unit has been all about centripetal force and rotation. I found it to obtain a lot more information in a shorter amount of time to learn it than most other units this year. I believe that I had most trouble understanding the concept of center of mass, but am now able to understand it due to the review questions my class made. I think that I could have been more thorough when answering homework questions in this unit, that would have helped me understand the center of mass concept as well as the other concepts better and in a shorter amount of time.
Rotational/Tangential Velocity:
Rotational and tangential velocity are two terms determining speeds in rotational object. Rotational velocity is measured in rpm (rotations per minute) and determines the amount of rotations an object has every minute. Tangential velocity is the determined by distance over time an object rotates. If an object such as a carousel is spinning at a certain velocity and one person is near the axis of rotation while his friend is at the edge of the carousel, they would have the same rotational velocity but a different tangential velocity. The boy in the middle would be going slower than the boy on the outside because it takes less time and less distance to revolve around the axis of rotation. The boy on the outside has to have a greater tangential velocity so that he can have the same number of rotations as the boy on the inside of the carol. Another example is two connected gears that can be rotated by a handle connected to one. If these two gears are different sizes but are connected, the tangential velocity of the two will be the same and the rotational velocity will be different. If they have the same tangential velocity then it would take the smaller gear more revolutions to go the same distance as the larger gear.
Rotational Inertia:
Rotational inertia is the property of an object to resist changes in rotation. More mass does cause more inertia, but an objects rotational inertia is dependent on where the mass is located. When the mass of a rotating object is located nearer the axis of rotation, there is less rotational inertia making it easier to spin. When a dancer is turning in forte, she repetitively pulls her arms and leg into her body to spin faster, but then spreads her arms and her leg out to slow down.
Conservation of Rotational Momentum:
The Conservation of Rotational Momentum states that the momentum of a rotating object is determined by the rotational inertia (RI) multiplied b the Rotational velocity (RV) so RI x RV=P. Also, the momentum of a rotating object before is equal to the momentum of the rotating object after, P before= P after. Therefore (RI x RV) before= (RI x RV) after. If there is a large rotational inertia and a small rotational velocity before then there is a large rotational velocity and a small rotational inertia after, RI x rv= RV x ri. This podcast helps to explain what the conservation of momentum is and how it works:
Torque:
Torque is what causes rotation, it is determined by the force(f) x the lever arm(la). When a force is applied to an object farther from the axis of rotation the torque is larger, so the torque is directly proportional to the force and the lever arm of an object. In order for an object to be balanced the clockwise and counterclockwise torque must be equal, so (f x la) clockwise=(f x la) counterclockwise. This also means that is the force is large and the lever arm is small on the clockwise side the the force will be small and the lever arm will be large on the counter clockwise side, (F x la)clockwise= (f x LA) counterclockwise.
Center of Mass:
The Center of Mass is the center position of all things mass. When the center of mass of an object is above the center of gravity, which is when gravity acts on the center of mass, it is balanced. The taller an object, the taller the center of gravity and the lower the center of mass the more balanced an object is. An example of this is a tight rope walker, he would carry a long drooping stick when on a rope to increase the lever arm and make the force smaller so that he would be more balanced. This can also be applied to a wrester, when they squat down and spread their knees they make their center of mass closer to the ground and create a larger base of support so that they are harder to push over.
Centripetal Force:
Centripetal force is the center seeking force that keeps you going into a curve. This is the only force acting on you, many believe that centrifical force is a center fleeing force that pushes you outwards but this force is fictitious and the reason you move outward is due to Newtons first law which states that an object in motion want to stay in motion and an object at rest wants to stay at rest, so when your car turns right your body wants to continue left. Centripetal force is what keeps a satellite in orbit, however there needs to be just enough initial velocity to get the satellite to continue in orbit otherwise it will crash into the earth or fly out into space.
In this photo the bull is rotating around in a circle with me on top. In order for me to stay on the bull, I moved my body to the middle of the bull and tucked my head and elbows into the middle so that my body would be over the center of gravity. This way I would spin with a lower tangential velocity and it would be easier for me to stay on the mechanical bull.
In class we were asked to find the mass of a meter stick using a 100g weight. I started by placing the meter stick on the edge of a flat table and put the 100g mass on the very end of the meter stick side that was off the table. I gradually moved the meter stick farther from the table until it became completely balanced with the weight on the end. Then I measured the distance from the mass to the table edge to find the lever arm. The entire meter stick is 100cm so the center of gravity would be at the 50cm mark. I subtracted the distance of the lever arm of the side off the table from the 50cm mark to find the lever arm of the other side of the meter stick. Once I found these components I used the torque equation where the torque of the left side would be equal to the torque of the right side (torque right=torque left). Torque is equal to the lever arm times the force to the final equation would be (Fxla)right=(Fxla)left. I plugged in the 100g mass to the force and the lever arm length off the table on the meter stick and made that equal to the lever arm of the side of the meter stick that was above the table time the variable x. Lastly I solved for x which gave me the mass of the meter stick!
This video uses illustrations to explain how torque works. Torque is equal to the lever-arm times the force of the rotating object. This video also gives example problems and clearly explains the math involved.
This video explains angular momentum and Rotational inertia by using everyday examples and visual experiments like spinning on a rotating stool. Angular momentum is conserved so the momentum before is the same as the momentum after. When a dancer is spinning with their arms stretched out, in order for her to spin faster and keep her momentum her speed must increase as she brings her arms into her chest. When the mass of an object is farther away from its axis, the rotational inertia increases making the rotation of the object slower, but when the mass is nearer to the axis the rotational inertia decreases making the object go faster.
This unit of Physics was relatively harder than the other two units this semester. First we learned about Newtons Third Law, which states that any action has an equal and opposite reaction. So if a car and a truck collide head on, then there is an equal amount of force exerted on each vehicle. This is also why if you hold a magnet out in front of a metal cart, the magnetic force of the magnet does not move the cart. Another example of Newtons Third Law is when a horse is pushing a buggy. In this example there are three action-reaction pairs; the force of the horse on the ground and the ground on the horse, the force of the horse on the buggy and the buggy on the horse, and the force of the buggy on the ground and the ground on the buggy. When the horse walks, it is pushing the ground back and the ground is pushing the horse forward. This is the same with the buggy and the ground, but since the force of the horse to the ground is greater than the buggy to the ground then the horse and buggy move forward! This can also be applied to the game of tug-o-war, the side with the greater force on the ground will be able to pull the rope to their side and win!
The next thing we learned about was vectors, a vector is a quantity having direction as well as magnitude, this may look like a line with an arrow. We used vectors to determine what direction a box would go in when on a ramp and what the force of tension would be on two ropes when holding up an object. In order to find the direction of a box on a ramp you would have to know the force of weight of the object (fweight), you would represent this with a vector pointing south of the box from the middle of the box. Then you would draw a vector north of that point with the same length as the fweight vector. After that, you would draw a line in any magnitude that is parallel to the ramp and touches the end of the vector that is north of the fweight vector. Then you would draw two perpendicular lines to the ramp and the line parallel to the ramp, one that goes through the point in the center of the box and one that starts at the bottom of the fweight vector. Lastly, you would draw a line that starts at the top of the perpendicular line on the center of the box and make it parallel to the fweight vector. Draw a vector from the point in the middle of the box to the point where that line and the perpendicular line starting at the bottom of the fweight meet and that is the direction the box is moving! This video should explain it much better than I did, it also explains how the force of tension can be found:
Next we learned about the Universal Gravitational Force which states that everything with mass attracts anything else with mass. The formula is:
gravitational force=[(mass1xmass2)/distance (squared)]universal gravitational force or
F=[(m1m2)/d^2]G. The universal gravitational force or G is always equal to 7x10^-11.One question that we had to answer was whether something would weigh more at the bottom of the ocean or at the top of Mt. Everest? The answer is that something would weigh more at the bottom of the ocean because of the distance, so the greater the distance the less something would weigh. Distance is a key factor in this equation.
I think that the most interesting thing that we learned about in this unit was tides. In one day there are approximately 4 tides, two low and two high. This is due t the gravitational pull of the moon, wherever the moon is there are high tides on either side of the earth, the two sides of the earth, however, will experience a different force. It takes 27 days for the moon to revolve around the earth completely. When the moon is directly in front of the sun and when the moon and the sun are on opposite sides of the earth there is a spring tide, these tides are higher than usual. When the moon is not directly in front of the sun or behind the earth but adjacent to the earth there are neap tides which are lower than usual.
After tides we learned all about momentum and impulse! Momentum is inertia in motion, Momentum (P)=mass(m)xvelocity(v)and the units are kgm/s. Impulse(J) is the quantity of force(F) x change in time(delta t). the change in momentum is: deltaP=(mv)final-(mv)initial which is also equal to the impulse. The impulse of an object is dependent on time, so if a skateboard was moving for five seconds and a train was moving for one second, then the skateboard would have more impulse, thus more momentum. This information can also be used to explain how an airbag keeps you safe:
P=mv
deltaP=(mv)final-(mv)initial
You go from moving to not moving in a car crash, therefor the change in momentum is the same whether you hit the dashboard or the airbags.
J=deltaP
Therefor the impulse is the same whether you hit the dashboard or the airbags.
J=F delta t
Since J is the same the airbags increase the time and the force must be less. Small force =less injury
After Momentum, we moved on to the conservation of momentum which is the change in momentum before is equal and opposite to the change in momentum after. This relates to newtons third law by this:
[a=after b=before]
Fa=-Fb (Newtons 3rd Law)
Fa delta t= -Fb delta t
Ja= -Jb
deltaPa= -deltaPb (conservation of momentum)
This formula helped explain why car bumpers are now plastic rather than rubber. When they were rubber, cars would bounce off one another, decreasing the time of impact. When the impact time decreases, the injury is much greater, so by making the bumper plastic you increase the time of impact.
I found it most difficult to understand the conservation of momentum and how impulse worked. By making this blog I think I understand it more than I did in class! I think i overcame these difficulties by making this blog and by asking questions on review days to Mrs. Lawrence. Also, I watched did a lot of practice problems.
Although this was the hardest unit yet, I finally got a hold of it in the end. I think I could have been more diligent in class this unit, I wasn't as focussed as I could have been, but I understand the material. Next unit I hope to be more focussed than I was this unit and possibly study a little better for quizzes.
