PHYS1001 Physics (Regular)
Tutorial 6: Dynamics of Rotational Motion
Part A: Conceptual Questions
Question 1
Imagine you are standing on the edge of a children’s
playground merry-go-round, which is rotating
clockwise.
i) Where are you more likely to slide off the
merry-go-round, near the middle or near
the edge?
ii) If you walk in towards the centre of the
merry-go-round, what will happen to the
angular momentum and angular velocity of the system (you and the
merry-go-round)?
iii) If you stay at the edge and start to walk in the direction of the rotation,
what will happen to the angular momentum of the system?
iv) What will happen to your angular momentum and angular velocity?
v) What will happen to the angular momentum and angular velocity of the
merry-go-round?
vi) What would be different if you walked in the opposite direction?
If you’d like to test this out for yourself, there is a large spinning disk that you can
walk and sit on in Victoria park next to the Sydney University Camperdown campus.
Question 2
2007 Exam question 2, 5 marks out of 90 (10 minutes)
A solid sphere, solid cylinder, and thin hollow cylinder roll down an incline. All start
from rest and roll without slipping. Each has mass m and radius r. Despite losing the
same amount of gravitational energy in their descent, the three objects do not arrive
at the bottom with the same translational kinetic energy. This situation is often
analysed by the conservation of mechanical energy.
i)
Draw a free-body diagram of the forces acting on one of the rolling objects
(i.e. choose one).
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PHYS1001 Physics (Regular)
ii)
Justify the application of conservation of mechanical energy to this situation.
Your answer should consider the work done by all the forces acting on the
objects.
iii)
Given that the conservation of mechanical energy applies, carefully explain
how it is possible for the three objects to have different translational kinetic
energies at the bottom of the incline.
Part B: Demonstration Questions
Question 1. A loaded race.
Spheres and cylinders of various diameters and an inclined plane are available on the
demonstration table.
Do all the cylinders roll down with same speed?
Do all the spheres roll down with same speed?
Try rolling them down the incline and try to explain why some of them roll down faster
than the others.
Question 2. The rotating stool.
Sit on the stool and start rotating with equal weights held in your hands. Start with the
hands stretched and slowly bring your hands towards your chest. What do you
observe? Explain.
A student sits on a stool rotating with an angular speed ω while holding two equal
heavy weights at arm's length. Without moving anything else, the two heavy weights
are dropped to the ground.
What change, if any, is there in the student's angular speed?
Is angular momentum conserved? Explain your answers.
Part C: Problems
Question 1
As a professional physics team, your group has been called in by the Australian
Institute of Sport to help them design a better bicycle wheel. They are investigating
two different wheel designs. The first is a solid wheel of uniform density. The second
is a spoked wheel with very light spokes which has virtually all of the wheel’s mass
at the rim. Both wheels have the same mass and radius.
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PHYS1001 Physics (Regular)
i) For a given translational velocity, 𝑣, and assuming no slipping, which will be
greater for the solid wheel: its translational kinetic energy or its rotational
kinetic energy?
ii) What about for the spoked wheel at the same translational velocity?
iii) Which wheel will your group recommend and why?
Useful formulae: 𝐼!"#$ = 1⁄2 𝑀𝑅% , 𝐼&''( = 𝑀𝑅% .
Question 2
2006 Exam question 8, 10 marks out of 90 (20 minutes)
A door is 0.90 m wide, of mass 10 kg and hinged
so that it swings without friction about a vertical
axis. A bullet of mass 0.020 kg and speed 300 m.s1
is fired at the exact centre of the door and hits the
door perpendicular to the plane of the door. The
door swings open when the bullet hits. Note: the
moment of inertia of a door of mass M and width d
about its hinged edge is 1/3𝑀𝑑 ! .
i) What is the angular momentum of the bullet
about the central hinge just as it hits the door? (Ignore the thickness of the
door.)
ii) What is the angular speed of the door just after the bullet hits?
iii) What is the total kinetic energy of the door and bullet just after the bullet hits
the door? Is kinetic energy conserved in the impact? Justify your answer.
iv) What would the angular speed of the door be if the bullet struck the outside
edge of the door (0.90 m away from the hinge)?
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PHYS1001 Physics (Regular)
Question 3
2005 Exam Question 8, 10 marks out of 90 (20 minutes)
A yo-yo is made from 2 uniform disks, each with mass m and radius
R, connected by a massless rod of smaller radius r. A thin string,
also massless, is wound several times around the connecting rod.
You hold the string and release the yo-yo from rest, which then
drops as the string unwinds without slipping.
i) What is the moment of inertia of the yo-yo?
ii) What is the relationship between the linear and angular
acceleration of the yo-yo?
iii) What is the linear acceleration of the yo-yo, in terms of the yo-yo parameters
(m, R and r)?
iv) What is the angular acceleration of the yo-yo, in terms of the yo-yo
parameters?
v) What is the tension in the string?
Extra question 4
Consider an Atwood’s machine (shown) with one block of mass
𝑚" = 500.0 g and the other 𝑚! = 460.0 g. The pulley, which is
mounted in horizontal frictionless bearings, has a radius of 50.0
mm. The pulley has a mass and so the tension in the two parts of
the rope is different. When released from rest, the heavier block
falls 75 mm in 5.00 s (without the cord slipping on the pulley).
i) Describe the motion of the blocks when they are released
from rest.
ii) Describe the motion of the pulley. What causes it to
accelerate?
iii) What is the acceleration of each block?
iv) What is the tension in the part of the cord that supports the heavier block?
v) What is the tension in the part of the cord that supports the lighter block?
vi) What is the angular acceleration of the pulley?
vii) What is the moment of inertia of the pulley?
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