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Rotation recap

Our last unit in AP physics c was rotational motion. In this unit we learned about rotational kinematics, dynamics and momentum. Rotational kinematic is very similar to translational kinematics because the same kinematic equations are used. The difference is that instead of displacement roation has the change in the angle. Instead of translational velocity and acceleration, rotational motion is calculated with angular velocity and acceleration.

As far as dynamics go, rotational motion has a very significant concept that separates it from translational motion. It's moment of inertia. Moment of inertia is the measure of an objects abilty to resist rotational motion. It could be compared to inertial mass or just mass. The other importance to rotational dynamics is the concept of torque which is a force that causes rotation mesured in Newton*meters. Torque is equal to the moment of inertia of the rotating object times its angular acceleration. Torque is also equal to the cross product of force and the distance from the axis of rotation that force is applied. Rotational dynamics is important for solving many different problems involving rotation.

Rotational or angular momentum is the measure of how difficult it is to stop a rotating object. It can be calculated using the equation L = moment of inertia * angular velocity. Angular momentum is also equal to the cross product of the objects radius and its translational momentum. It is important to know that angular momentum is always conserved, so in a closed system the intitial angular momentum is equal to the final angular momentum. 

Rotation is a very important topic because it is so useful in the world of science and engineering because not everything moves in linear motion. For instance our solar system can be studied using rotation since our planets move in rotational paths.

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Top Lab

 

The Engineering design process is a series of steps that engineers go through to create a product of some sort. The process can be very repetitive at times while going through a process of trial and error. The lab that we did in class demonstrated the engineering design process. We were given two paper plates, six pennies, a pencil, and tape to create a spinning top. First we came up with an idea that we thought might work so we constructed a top that had a pencil through the center of a plate with six penny's evenly spaced around the plate but not to the edge. The plate was at about the center of the pencil. This failed because the plate was not stable enough on the pencil so we added the other plate to the bottom of the first plate to stabilize it a little more. We also lowered the location of the plate to be more toward the bottom of the pencil. This would decrease the wobbling because there would be less torque on the pencil if there is a smaller distance since Torque is the cross product of F * r. These two adjustments improved the top but it still was not spinning perfectly. Something that would have made it spin a lot better would be to shorten the length of the pencil. This would have gotten rid of the weight at the top of the pencil to decrease the net torque even more.

Moment of inertia was a big part of this lab because moment of inertia is an object's resistance to rotational acceleration. An object with the least possible moment of inertia would be the most successful. 

Angular momentum was also a very important part of this lab because angular momentum describes how difficult it is to stop a rotating object. Therefore, an object with the greatest angular momentum would be very successful in this lab because it would take a lot of torque to change it. 

baseball00

Micheal Jordan didn't get the nickname "Air Jordan" for nothing. He is known for his ability to jump really high in order to perform epic slam dunks. How does he do this?

Micheal Jordan stands 1.98 m tall and has a wingspan of 2.13 m. A basketball hoop is 3.05 m high; therefore, he has to jump about .16 m above the ground for his hand to reach the rim. Jordan is most famous for his dunk from the foul line which is 4.57 m from the basket. In order for him to successfully complete this projectile, he must jump with an initial velocity of 25.31 m/s from the ground; 1.77 m/s in the vertical direction and 25.25 m/s in the horizontal direction. 

In order to produce this velocity he must push of from the floor with a force of 1454 N if he pushes off of the ground for .2 seconds. 

 

baseball00

What makes us move? Well that's obvious. It's our feet, but how exactly does that happen. The answer is newtons third law of motion: when a force is applied to one object, that object automatically applies that same force back. 

:jig: 

When your foot presses on the surface of the earth at an angle, the earth pushes back on your foot with the same force causing your body to accelerate forward. You might say, well then why does the earth not accelerate. That's because the earth is so big compared to your body that the force that you push on the earth with is practically nothing. 

You can also tie this to conservation of momentum. If you and the earth both start at rest and a force is applied to accelerate your body, the earth body system's momentum is conserved. 

baseball00

The last unit we studied in AP Physics C was Work, Energy and Power. First we reviewed the concept of work and how it equal to force*displacement. In a calculus based physics class however Work is also equal to the integral of force with respect to displacement. This means that the area under a Force vs Displacement graph is equivalent to the work done on the object. We also learned about Hooke's law and how it describes the relationship between the force of a spring and displacement. The slope of a graph of force vs displacement represents the opposite of the spring constant (k) of the spring. From this the equation F= -kx was determined. Then we analyzed the work energy theorem which shows that work is equal to the change in kinetic energy. 

Kinetic energy is the energy of an object that is moving. Potential energy is stored energy that an object has the potential to use. In a closed system energy is conserved. The total energy of a system is equal to the potential energy plus the kinetic energy.

Power is a measure of the rate at which work is done, therefore power equals Work/time. From this we can also conclude that power is also equal to force*velocity. This unit will be helpful in many ways. It is an alternative to many kinematic problems and will also be helpful in other topics as well.

baseball00

The Hubble Space Telescope is a large telescope that was launched into space in 1990 and has been used to see images that were, before Hubble, too far to see. Just recently, on October 20th, Hubble captured an image of a twisted cosmic knot in the constellation cancer as shown in the image below. This is 250 million light years away. A cosmic knot is what occurs when two galaxies collide to form a new galaxy. This galaxy, NGC 2623, stretches approximately 50000 light years from end to end. When galaxies merge, star clusters begin to form which is shown by the specks of bright blue that exist throughout the twisted cosmic knot. These newly formed clusters are blue because the blue stars inside the cluster are much hotter than the other stars. As time goes on the clusters will change to red because the blue, hotter stars will die out faster. Hubble has been extremely useful in the world of astronomy for discoveries like NGC 2623 and many others. Its groundbreaking technology has helped us to significantly improve our understanding of the universe.

NGC 2623

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As I was scrolling through Instagram, I came across a post by Nasa that said today, October 14th, 2017, is the 70th anniversary of supersonic flight. Supersonic flight is when something is traveling faster than the speed of sound, which is 343 m/s. Of course for the past 70 years this has only been done by noncommercial planes. Well, Nasa is currently working on making supersonic flight a reality for commercial planes. That would mean that you can travel from New York to Los Angeles in 2 hours. Now it takes over 6 hours. Nasa has been researching shock waves, cruise efficiency, and the effect of sonic booms on the environment. Sonic booms are loud boom sounds caused by the waves of sound. It occurs when an object travels at supersonic speed. If Nasa is able to make this a reality in will revolutionize modern travel.

baseball00

This weekend I watched a lot of football. Watching it this week made me realize how bad it must hurt to get hit by a 240+ pound linebacker. The average running back runs about 4.72 m/sec and has a mass of about 97.5 kg. If the linebacker stops the running back in 1 second, the force on the running back is about 460 newtons. Due to newtons third law, that same force is thrown onto the linebacker as well. A linebacker that is famous for his powerful tackles is James Harrison for the Pittsburgh Steelers. He is 125 kg... Sometimes football is better to be watched then played. 

baseball00

During this week in AP Physics C, we have begun our studies in Dynamics. At first it was not too bad... then came air resistance. It seems like a pretty simple concept but it is in fact not. I don't have much experience in Calculus yet, so the differential equations are still pretty difficult to understand. There is still a good amount of time before the test for me to study this concept so hopefully I will get a good grasp on it before the test. Other than the differential equations, the confusing part for me is why there are two equations for Fdrag which are Fdrag = bv and Fdrag = cv2 . Why do some circumstances use one equation and others use the other equation? Even though this concept is really difficult, I think it is extremely important for accurate calculations. In past physics courses we have always neglected air resistance but here on earth there is usually air all around. 

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