Kinesiology 2241A/B Lecture Notes - Lecture 21: Moment Of Inertia, Angular Velocity, Momentum

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copperlizard489

14 Mar 2018

School

Western University

Department

Kinesiology

Course

Kinesiology 2241A/B

Professor

Thomas Richard Jenkyn

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Angular momentum is the rotational inertia of an object multiplied by its angular velocity. Your magnitude and direction are the same while in the air until you hit the ground. Similar to linear momentum, this is the quantity of rotational motion in the object: Angular momentum is a measure of how hard it will be to stop the object rotating. Your axis of rotation is going to be the same while in the air until you hit the ground. Remember the radius of gyration and how we use it to find the rotational inertia. But how does angular momentum relate to torque. To change angular momentum we need to apply a torque (similar to linear momentum needs a force) You have no torque on you while you"re in the air, however as long as you have a foot on the ground you can correct your torque so that you land how you need to.

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In order to solve the problem you must refer to the first partwhich i already solved and I am 200% sure of the answers, however Iam stuck on the second part and I need help asap. Please do not getscared when you look at this problem and thank you soo much inadvance.

A wheel 75 meters in diameter is mounted vertically on an infinitefrictionless plane at the origin. The infinite frictionless planehas a grid of Cartesian coordinates on it. The moment of inertia ofthe wheel is mr^2. The mass of the wheel is 2000kg. There is anengine connected to the wheel that can produce a torque of 2.34x10^6 Nm. There is a 50 kg object attached to the circumference ofthe wheel that is attached to the wheel with a remote releasemechanism. The wheel is placed on the origin so that the plane ofthe wheel contains the point x=50 meters and y=86.8 m. The wheel ispositioned so that the object is just above the plane at the 6o'clock position. The engine is engaged and begins to apply thetorque to the wheel at 12:00 noon on March 1, 2011. The wheelbegins to rotate in the counterclockwise direction. The torque isapplied for 4 x 10^4 revolutions. At that point the object isreleased from the wheel and a 75 Newton motor accelerates theobject in the direction it is released. The motor is fired for 2.34x 10^4 seconds. (the following questions i have already answered)What is the angular velocity and rotational KE of the object justbefore it is released? (answer for that is 6.39 x 10^2 rad/sec and5.89 x 10^11 J). What angle does the path of the object make withthe x axis? (answer is 60.05 degrees). Where is the object on theinfinite frictionless plane when the motor stops (what are itscoordinates....answer is x=4.85x10^8m y=8.40x10^8m). What is thevelocity and linear KE of the object when the motor stops?(5.91x10^4 m/sec and KE= 8.73 x 10^10J). How much work was done onthe object up until the time the motor stopped? (8.73 x 10^10J).(Hint: the mass of the wheel is 2050 kg while the torque is appliedand the object is attached).

YEA I know what you are thinking at this moment. Difficult right?Please give it a chance and have faith in yourself. Here is thepart I had difficulty with:

After the engine stops firing the object is turned around so thatthe engine can be used to stop the object. The motor is fired atits rated thrust to stop the object. Unfortunately it malfunctionsand shuts down after an hour and the object coasts from then on. Atthe end of an hour of coasting it encounters a ramp that is 2000meters high and slopes up at an angle of 20 degrees. The objectclimbs the ramp and flies off the ramp into the air when it reachesthe end of the ramp. It strikes the plane and digs a crater 5meters deep in the plane and comes to a stop. How far from the endof the ramp does it land? Where does it land on the plane (as incoordinates)? What is the resultant velocity of the object and whatis the acute angle of the resultant velocity with the plane when itstrikes the plane? What is the KE of the object when it hits theplane? What date and time is it when the object lands on the plane?How much work was done on the object to stop it? How long did ittake to stop? What was the deceleration of the object in m/sec^2?What was the force on the object in Newtons to stop it?

If you are from MIT I have faith that you can do this. I am only ajunior in high school taking first year physics that is not evenAP. My teacher is from MIT and said he did this kind of stuff whenhe was there. Please please please help me! I'm desperate.

Kinesiology 2241A/B Lecture Notes - Lecture 21: Moment Of Inertia, Angular Velocity, Momentum

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