# Physics

Is the mngnitude of the center-of-nutss acceleration of spool A (while it is fallin g) greater than,less than, or equal to that of spool B? Explain.

Is the translational kinetic energy of spool A just before it hits the ground greater thsn, less than, or equal to that of spool B? Explain.

d. Is the total kinetic energy of spool A just before it hitsothe ground greater than, less than, or equal to that of spool B? Explain.

Consider the system consisting of all of these objects: spool A, spool B, the thread, the pulley, and the Eafth.

i. Explain how you can tell that the total energy of this system(i.e., Ugnv,o+ Ug^”,n * Kton,,e * K,*nr. n * Kro’ a, * K,o’ s) is constant as spools A and B fall.

b.

c.

Tutorials in Introductory Physics McDermott, Shaffer, and the P.E.G., U. Wash.

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Dynamics of rtgtd bodies Narne Mech HW-73

Suppose that this system starts with Ugo”, o = f/srr, B = 9 J. Just before the spools hit the ground, which is where the zero for gravitational potential energy is chosen, spool A has translational kinetic energy K,on,”a = 4 J. Determine the value of the rotational kinetic energy of spool A at this instant. Show your work.

6. A third identical spool, spool C, is added to the falling-spools experiment described in the preceding problem.

As above, all spools are released from rest from the same height at the same instant. Spool C is not in contact with any other objects as it falls.

a, Rank the spools according to magnitude of center -of-mas s acc eleration (while falling), from largest to smallest. If any spools have the same center-of-mass acceleration, state so explicitly. Explain.

b. As in the preceding problem, suppose that Ugrrr. n = Ugr,, s = 9 J before the spools are released. Just before the spools hit the ground, which is where the zero for gravitational potential energy is chosen, spool A has trarrslational kinetic energy K,*,, e,= 4J.

i. Rank the spools according to maximum tanslatianal kinetic energy, from largest to smallest. If any spools have the same maximrrtn translational kinetic energy, state so explicitly. Explain. (Use the definition K*, = lma”^’.)

ii. Rank the spools according to maximum total kinetic energy, from largest to smallest. If any spools have the same maximum total kinetic energy, state so explicitly. Explain.

Tutorlals in Introductory Physics McDermott, Shaffer, and the P.E.G., U. Wash.

I arson Custom 2nd Ed., for U.CO, Boulder

CONSERVATION OF ANGULARMOMENTUM

Name Mech HW-77

1. In tutorial, you observed the following three experiments involving a student sitting at rest on a stool, holding a spinning bicycle wheel as shown at right:

Experiment 1: The student places his arm against the side of the wheel, slowing it to half its initial angular speed.

Experiment 2: The student places his arm against the side of the wheel, bringing it to a stop.

Experiment 3: The student quickly flips the wheel over (so that it is spinning clockwise when viewed from above, with the same angular speed it had initially).

Student initially at rest

Initial sense of wheel’s

rotation

a. You observed that the final angular speed of the student in experiment 3 is greater than that in experiment2, Account for this result using the ideas developed in the tutorial.

b. Rank the experiments according to final kinetic energy of the wheel, from largest to smallest. If the final kinetic energy of the wheel is the same in any two experiments, state so explicitly. (Hint: Can kinetic energy ever be negative?) Explain.

Rank the experiments according to final kinetic energy of the student, from largest to smallest. If the final kinetic energy of the student is the same in any two experiments, state soexplicitly. Explain.

d. Rank the followingfour quantities from largest to smallest: the initial kinetic energy of the wheel (K*i) and the final kinetic energy of the student-wheel system in experiments 1 ,2, and 3 (Kstr, etc.). Explain. (Hint: It may be helpful to think about changes in energy other than mechanical energy.)

Tutorials in Introductory Physics McDermott, Shaffer, and the P.E.G., U. Wash.

earson

Custom 2nd Ed., for U.CO, Boulder

– Mech

HW-78 Conseruation of angular momentum

Z. The diagram below illustrates four hypothetical collisions that take placg on a level, frictionless surface.- The collisions are shown from a top-view perspective. All pucks are identical. If a linear or angular velocity is not specified, it is zero. If distances appear to be equal, assume that they are.

For each hypothetical collision:

a. Specify the direction of the angular momentum of the rod-puck(s) system with respect to the center of the rod both before and after the collision. If necessary, use the convention that a vector into the page is represented by the symbol I and a vector out of the page is represented by the symbol O.

b, Specify the direction of the linear momentum of the rod-puck(s) system, both before and after the collision.

c. On the basis of your answers above, state whether each hypothetical collision could ot could not occrfi. If a particular hypothetical collision could not occur, state whether it violates (l) the principle of conservation of linear momentum, (2) the principle of conservation of angular momentum, or (3) both.

Before collision

Case I

Case 2

Case 3

Case 4

Ball sticks to

rod

Sense of rotation

After collision

Tutorials in Introductory Physics McDermoff, Shaffer, and the P.E.G., U. Wash.

@ son Custom ?od EA., for U.CO, Eoulder

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