torque dynamics problems

jones (jj25597) – Torque dynamics – campbell – (53073) 1

This print-out should have 12 questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.

001 10.0 pointsA cord is wrapped around a flywheel of inertia

I =1

2mR2 and radius R . A mass m is

suspended by the cord. The system is releasedfrom rest and the suspended mass falls.

R

I

ω

m

T

g

What is the acceleration of the suspendedmass m?

1. a =1

2g

2. a =1

4g

3. a =3

2g

4. a = g

5. a = 2 g

6. a =2

3g

002 (part 1 of 2) 10.0 pointsA small, solid sphere of mass 0.5 kg and

radius 50 cm rolls without slipping along thetrack consisting of slope and loop-the-loopwith radius 1.1 m at the end of the slope. Itstarts from rest near the top of the track at aheight h, where h is large compared to 50 cm.The acceleration of gravity is 9.8 m/s2 .Hint: The moment of inertia for a solid

sphere is2

5m r2 .

P

1.1 m

50 cm

0.5 kg

60◦

h

What is the minimum value of h (in termsof the radius of the loop R) such that thesphere completes the loop?Answer in units of m.

003 (part 2 of 2) 10.0 pointsWhat are the force component in the hori-zontal direction on the sphere at the point P,which has coordinates (−R, 0) if we take thecenter of the loop as origin, and if h = 3R ?Answer in units of N.

004 (part 1 of 3) 10.0 pointsA string is wound around a uniform discwhose mass is 2.6 kg and radius is 0.58 m ,see figure below. The disc is released fromrest with the string vertical and its top endtied to a fixed support.The acceleration of gravity is 9.8 m/s2 .

h 0.58 m

2.6 kg

ω

As the disc descends, calculate the tensionin the string.Answer in units of N.


005 (part 2 of 3) 10.0 pointsCalculate the magnitude of the accelerationof its center of mass.

1. acm = 7.252 m/s2

2. acm = 5.94533 m/s2

3. acm = 5.684 m/s2

4. acm = 6.53333 m/s2

006 (part 3 of 3) 10.0 pointsAfter starting from rest, calculate the speedof its center of mass when the center of masshas fallen ∆h = 1.1 m.Answer in units of m/s.

007 10.0 pointsConsider a basketball rolling (without slip-ping) down an inclined plane. The basketballis basically a thin spherical shell, so its mo-

ment of inertia I =2

3M R2.

Given the angle of 15.1 ◦ between the in-cline and the horizontal, calculate the basket-ball’s center’s acceleration. The accelerationof gravity is 9.8 m/s2 .Answer in units of m/s2.

008 10.0 pointsA 2.03 kg hollow cylinder with inner radius0.11 m and outer radius 0.48 m rolls with-out slipping when it is pulled by a horizontalstring with a force of 26.4 N, as shown in thediagram below.

26.4 N2.03 kg

ω

0.11 m

0.48 m

What is the acceleration of the cylinder’scenter of mass? Its moment of inertia about

the center of mass is1

2m

(

R2

out +R2

in

)

.

Answer in units of m/s2.

009 10.0 pointsTwo wheels with fixed hubs and radii 0.78 mand 1.2 m, each having a mass of 3 kg, startfrom rest. Forces 4 N and F2 are appliedtangentially to the smaller and larger wheels,respectively.

b

4 N

R = 0.78 m

b

F2

R = 1.2 m

In order to impart the same angular accel-eration to each wheel, how large must F2 be?Assume that the hubs and spokes are mass-less, so that the rotational inertia is given byI = mR2.Answer in units of N.

010 (part 1 of 2) 10.0 pointsA spool of wire of mass 3.2 kg and radius0.33 m is unwound under a constant wiretension 9.2 N. Assume the spool is a uniformsolid cylinder that rolls without slipping.

R

F

M

Find the friction force on the bottom of thespool. Let right be positive.Answer in units of N.

011 (part 2 of 2) 10.0 pointsCalculate the acceleration of the spool’s cen-ter of mass.Answer in units of m/s2.

012 10.0 pointsA wheel of radius 59 cm, mass 4 kg, andmoment of inertia 0.6962 kg ·m2 is mounted


on a frictionless, horizontal axle as in thefigure. A light cord wrapped around the wheelsupports an object of mass 1.4 kg .

59 cm

4 kg

ω

1.4 kg

T

Find the tension T in the cord. The accel-eration of gravity is 9.8 m/s2 .Answer in units of N.

torque dynamics problems

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