Workshop Tutorials for Technological and Applied Physics
MR10T: Rotational Dynamics II
A. Qualitative Questions:
1. Imagine standing on the edge of a merry-go-round. The merry-go-round is rotating clockwise.
a. Where are you more likely to slide off the merry go
round; near the middle or near the edge?
b. If you walk in towards the centre of the merry-goround, what will happen to your angular momentum
and angular velocity?
c. 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 (you plus the merrygo-round)?
d. What will happen to the angular momentum and
angular velocity of the merry-go-round?
e. What will happen to your angular momentum and
angular velocity?
f. How would it be different if you started to walk in
the opposite direction?
2. One of the most popular forms of entertainment in the world is sport, and millions of dollars are spent
developing better tennis racquets, lower friction swimming suits, harder to detect performance enhancing
drugs and more efficient bicycles. As a professional physicist you’ve been called in by the Australian
Institute of Sport to help them design a better bicycle wheel. There are two designs that they’re
investigating. The first is a solid wheel of uniform density, and the second is a spoked wheel with very
light spokes so that virtually all the mass of the wheel is at the rim. Both wheels have the same mass and
radius.
a. For a given translational velocity, assuming no slipping, which will be greater for the solid wheel; its
translational kinetic energy or its rotational kinetic energy?
b. What about for the spoked wheel at the same translational velocity?
c. Which wheel will you recommend that they use and why?
(note: Idisc = ½ MR2, Ihoop = MR2)
B. Activity Questions:
1. The rotating stool
Sit on the stool and start rotating with equal weights held in your hands.
Start with the hands in close to your chest and slowly stretch your hands outwards.
What do you observe?
What happens when you pull them back in again? Why?
The Workshop Tutorial Project –MR10T: Rotational Dynamics II
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2. Falling cats
The diagram on display shows how a cat can rotate itself around
so that it always lands on its feet. Sit on the rotating stool and see
if you can turn yourself around the way a cat does.
How is it possible to do so without violating conservation of
angular momentum?
3. Bicycle wheel
Spin up the bicycle wheel. What do you feel when you try to tilt the wheel?
Carefully hand the wheel to someone sitting on the rotating stool.
What happens when they tilt the wheel? Why?
C. Quantitative Questions:
1. A merry go round can be described as a horizontal platform in the shape of a disc which rotates on a
frictionless bearing about a vertical axis through its centre. The platform has a mass of 150 kg, a radius of
2.0 m and a rotational inertia of 300 kg.m2. A 60 kg student walks slowly from the rim of the platform
toward the centre. If the angular speed of the system is 1.5 rad.s-1 when the student starts at the rim, what
is the angular speed when he is 0.5 m from the centre?
2. The figure shows two disks, one an engine flywheel, the other
a clutch plate attached to a transmission shaft. Their moments of
inertia are IA and IB; initially, they are rotating with constant
angular velocities A and B, respectively. We then push the
disks together with forces acting along the axis only, so as to
keep their faces parallel. The disks rub against each other and
eventually reach a common final angular velocity, .
a. Derive an expression for .
Suppose the flywheel A has a mass of 2.0 kg, a radius of 0.20 m,
and an initial angular velocity of 50 rad.s-1 and the clutch plate B
has a mass of 4.0 kg, a radius of 0.10 m, and an initial angular
velocity of 200 rad.s-1.
b. Find the common angular velocity, , after the disks are
pushed into contact.
c. Is kinetic energy conserved in this process?
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The Workshop Tutorial Project –MR10T: Rotational Dynamics II
B
A
IA
IB

IA + IB