Homework #10 Physics 1112
References: Chap. 10, sections intro., 10.2, 5, 6 Physics Ideas:
Math Skills: Spring 2015 Vector Rotational Mechanics
Angular Momentum & Torque
Geometry, Trigonometry, Algebra, Calculus
Vector Geometry, Algebra, Components, & Cross Product Learning Goals: (Be sure you understand where and how each goal in each assignment applies to our
homework, discussion, lecture, and lab activities.) *
*
*
*
* Define angular momentum, and calculate it for objects moving through space and/or
rotating.
State the basic relationship between angular momentum and torque, and use it to determine
how angular momentum of a system changes.
Tell when angular momentum of a system is conserved, and use the principle of
Conservation of Angular Momentum to calculate and relate changes in the motion of an
object or system of objects.
State the basic relationship between angular momentum and torque, and use it to determine
how angular momentum of a system changes.
Tell when angular momentum of a system is conserved, and apply the principle of
Conservation of Angular Momentum when appropriate.
Show that algebraic & numerical results have correct units and are physically reasonable. sh is
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m * For extra practice: Chapter 10: Qs #Q10.20, 22, 24-27; Es & Ps #10.43, 47, 51, 89, 95, 97, 99
(not turned in)
#10.42 [Block on Table] Please add: (e) Show that the linear speed of the block has also
increased. What supplies energy to the block to increase its speed and kinetic energy?
#10.46 [Mud on Door] Please add: (b) How would the mud's moment of inertia be included?
To be turned in to your Discussion instructor’s HW box by 4 PM on Friday, April 10: Th #10.41 [Neutron Star] Please add: (b) What is the rotation period of the neutron star? How
many times does it rotate in one second? (c) Show that the star's rotational kinetic energy has
increased, and determine by what factor. What provides the added kinetic energy?
2
[HINT: Show that you can write the star's KE as K = L /2I, where L and I are angular
momentum and moment of inertia.]
#10.45 [Parachutist on Turntable] Please add: (c) Is horizontal linear momentum of the
parachutist + turntable conserved here? Why or why not?
[Assignment CONTINUES on next page] https://www.coursehero.com/file/14145352/10pdf/ #1. [Atwood Machine] Two blocks A and B with masses mA and mB (> mA)
hang from a light string passing over a uniform solid cylindrical wheel without
slipping. The wheel's mass is M, it's radius is R, and friction due to its axle is
negligible. The blocks are released from rest at the locations shown. In a
previous HW problem, we analyzed this system using Conservation of Energy
and Newton's 2nd Law for Rotation. Here, we'll analyze this problem by angular
momentum considerations B (a) Draw a free-body diagram showing all the external forces acting on the
system of 2 blocks + wheel + string. Be sure that you show only external forces
for this system, not internal forces acting within the system.
(b) Write an expression for the net external torque acting on the system of the
blocks + wheel + string about the wheel's axle. What is its vector direction? sh is
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m (c) Write an expression for the magnitude of the system's total angular
momentum about the wheel's axle when each block is moving with speed v and
the wheel has corresponding angular speed ω . What is the vector direction of
this angular momentum? What is the kinematic relationship between v and ω ? A (d) Write the relation between the net external torque and total angular momentum from the
previous parts, and use it to obtain an expression for the acceleration of each block. Check your
results with Problem #1 on HW #9.
#2. [Rolling Spool] A spool on a horizontal surface with friction can
be pulled by a string wrapped around the middle of its axle. For each
case below (a-c), in which direction will the spool roll when the string is
pulled gently? Be sure your reasoning is clear. [HINT: Consider the
!
! dL
relation " ! !=!
about the point on the ground midway between the
dt
contact points of the spool's wheels with the surface. Refer to your lecture notes to recall how
the spool's translational and rotational angular momentum about that point are related.]
(b) (c) Th (a) (d) Show that there is a direction in which the string can be pulled gently so the spool slides
along the surface without rotating. Illustrate this direction on a diagram, and show how to
determine an expression for the angle the string makes with the vertical. Be sure your
reasoning is clear.
[Assignment CONTINUES on next page] https://www.coursehero.com/file/14145352/10pdf/ #3. [Colliding Sticking Disks] Two identical uniform solid disks, each of mass M and radius
R, can slide on a horizontal frictionless surface. Disk A is initially moving with speed vo
without spinning. Disk B is initially at rest without spinning. Disk A approaches disk B and
makes grazing collision with B so their edges just barely touch and then stick together. The
disks then proceed to slide stuck together while spinning about their contact point.
(a) Which of these physical quantities
do you know are conserved in this
collision, and which are not: linear
momentum, kinetic energy, angular
momentum? Why?
(b) What is the final speed of the centerof-mass (CM) of the stuck-together disks? A vo Before ω A
B (c) What is the moment-of-inertia of the stuck-together disks about their CM?
[HINT: You'll need to use the Parallel-Axis Theorem for each disk + superposition.] vCM B After (e) sh is
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m (d) What is the angular speed of rotation of the stuck-together disks? [HINT: You can consider
the motion as seen in the CM reference frame—the reference frame in which the CM is at rest.]
What fraction of the initial kinetic energy (KE) remains as total KE after the collision? Th (f) In order for the two stuck-together disks not to rotate after they collide, in which sense (CW
↻ or CCW ↺) should the incoming disk be rotating? What should its initial angular speed be? https://www.coursehero.com/file/14145352/10pdf/ Powered by TCPDF (www.tcpdf.org)

 

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