PHYS 211 Lecture Notes - Lecture 21: Spinning Wheel, Angular Momentum

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cerisegiraffe538

4 May 2015

School

University of Illinois

Department

Physics

Course

PHYS 211

Professor

Mestre

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Document Summary

Phys 211- lecture 21- angular momentum and precession. Consider a mass attached to a massless string that is fixed to a pivot on a table. The string is rotating horizontally so that the mass moves in a circular path on the table. Now imagine that there is a small motor at the pivot point that slowly shortens the string as the mass continues to move, thus slowly reducing the radius of rotation. The answer is yes, angular momentum is conserved. Tension will not create torque because the tension force is acting in a parallel direction to the radius of rotation. Therefore, the net external torques equal zero and angular momentum is conserved. The following ratios are useful for evaluating how changes in the system (i. e changing the radius of rotation) can change internal changes. Remember that angular momentum has direction as well as magnitude.

Related Questions

An oversized yo-yo is made from two identical solid disks each of mass M=2.00 kg and radius R=10.0 cm. The two disks are joined by a solid cylinder of radius r-4.00 cm and mass m=1.00 kg as in Figure P8.34. Take the cejter of the cylinder as the axis of the system, with positive torques directed to the left along this axis. All torques and angular variables are to be calculated around this axis. Light string is wrapped around the cylinder, and the system is then allowed to drop from rest. (a)What is the moment of inertia of the system?(b)What torque does gravity exert on the system with respect to the given axis?(c)Take downward as the negative coordinate direction. As depicted in Figure P8.34, is the torque exerted by the tension positive or negative? Is the angular acceleration positive or negative? What about the translational acceleration?(d)Write an equation for the angular acceleration in terms of the translational acceleration and radius.(e)Write Newton's second law for the system for rotation in terms of: m,M,a,T and g.

Which of the following statements are true? (Select allthatapply.)

1. For the total linear momentum of a system to be conserved,theremust be no external forces acting on the system.

2. The total linear momentum of a system may be conserved evenwhenthe mechanical energy of the system is not.

3. The velocity of the center of mass of a system changes onlywhenthere is a net external force on the system.

4. None of these statements are true.

I thought that the 1 was true because of the law of conservationofmomentum and 3 was true because if the total momentum of asystemremains constant, then the velocity of the center of mass ofthesystem remains constant, and you need an external force tochangemomentum.
I also though 2 was false.

However, I am being told this is wrong. Can someone clarify thisforme?

An oversized yo-yo is made from two identical solid disks each of massM=2.00kg and radius R=10.0cm. The two disks are joined by a solidcylinder of radius r= 4.00cm and mass m=1.00kg. Take the center of thecylinder as the axis of the system, with positive torques directed tothe left along the axis. All torques and angular variables are to becalculated around this axis. Light string is wrapped around thecylinder, and the system is then allowed to drop from rest. (a) What isthe moment of inertia of the system? Give a symbolic answer. (b) Whattorque does gravity exert on the system with respect to the givenaxis. (c) Take downward as the negative coordinate direction. Is theangular acceleration positive or negative? What about the translationalacceleration? (d) we an equation for the angular acceleration(alpha) in terms of the translation acceleration a and radius r. (e)Write Newton's second law for the system in terms of m, M, a,T, and g. (f) Write Newton's second law for rotation in terms of I, alpha, T, andr. (g) Eliminate alpha from the rotational second law with theexpression found in part (d) and find a symbolic expression for theacceleration a in terms of m, M, g, r, and R. (h) What is the numericvalue for the system's acceleration? (i) What is the tension in thestring? (j) How long does it take the system to drop 1.00m from rest?

PHYS 211 Lecture Notes - Lecture 21: Spinning Wheel, Angular Momentum

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