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A circular disk with moment of inertia 1/2 mR2, mass mand radius R is mounted at its center, about which it can rotate freely. A light cord wrapped around it supports a weight mg. Find the total kinetic energy of the system when the weight is moving at a speed v.

1. K = 3/4 mv2    
2. K = 1/2 mv2
3. K = 2/3mv2
4. K = 5/2 mv2
5. K = 1/3 mv2
6. K = 4/5 mv2
7. K =3/2 mv2
8. K = 5/4 mv2
9. K =mv2


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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

This problem illustrates the two contributions to the kinetic energy of an extended object: rotational kinetic energy and translational kinetic energy. You are to find the total kinetic energy Ktotal of a dumbbell of mass m when it is rotating with angular speed? and its center of mass is moving translationally with speed v. (Figure 1) Denote the dumbbell's moment of inertia about its center of mass by Icm. Note that if you approximate the spheres as point masses of mass m/2 each located a distance r from the center and ignore the moment of inertia of the connecting rod, then the moment of inertia of the dumbbell is given by Icm=mr2, but this fact will not be necessary for this problem.

 

Find the total kinetic energy K_tot of the dumbbell.
Express your answer in terms of m, v, Icm, and ?.

This problem illustrates the two contributions to

Two metal disks, one with radius R1 = 2.59 cm and mass M1 = 0.850 kg and the other with radius R2 = 5.08 cm and mass M2 = 1.61 kg, are welded together and mounted on a frictionless axis through their common center (Figure 1).

(A) What is the total moment of inertia of the two disks?

(B) A light string is wrapped around the edge of the smaller disk, and a 1.50-kg block, suspended from the free end of the string. If the block is released from rest at a distance of 2.10 m above the floor, what is its speed just before it strikes the floor?

(C) Repeat the calculation of part (B), this time with the string wrapped around the edge of the larger disk.

 

 

A string is wrapped around auniform disk of mass M = 1.2 kg and radius R = 0.07 m. (Recall thatthe moment of inertia of a uniform disk is (1/2)MR2.) Attached tothe disk are four low-mass rods of radius b = 0.11 m, each with asmall mass m = 0.5 kg at the end. The device is initially at reston a nearly frictionless surface. Then you pull the string with aconstant force F = 29 N. At the instant when the center of the diskhas moved a distance d = 0.039 m, a length w = 0.023 m of stringhas unwound off the disk.





(a) At this instant, what is the speed of the center of theapparatus?
v = ? m/s

(b) At this instant, what is the angular speed of theapparatus?
w1 = ? radians/s

(c) You keep pulling with constant force 29 N for an additional0.022 s. Now what is the angular speed of the apparatus?
w2 = ? radians/s

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