Transcript Document

Physics 1901 (Advanced)
A/Prof Geraint F. Lewis
Rm 557, A29
[email protected]
www.physics.usyd.edu.au/~gfl/Lecture
http://www.physics.usyd.edu.au/~gfl/Lecture
Rolling without Slipping
For a rolling wheel which does not slide, then the distance it
travels is related to how much it turns.
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Rolling without Slipping
The total kinetic energy is
and
Where C is the constant of the Moment of Inertia
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Rolling without Slipping
Conservation of energy
 Independent of mass & size
 Any sphere beats any hoop!
What is the source of torque?
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Rolling without Slipping
Torque is provided by
friction acting at the
surface (otherwise the
ball would just slide).
Note that the normal
force does not
produce a torque
(although it can with
deformable surfaces
and rolling friction).
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Rotational Work
In linear mechanics, the
work-kinetic energy
theorem can be used to
solve problems.
In rotational mechanics,
we note that a force,
Ftan, applied to a point
on a wheel always
points along the
direction of motion.
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Rotational Work
If the torque is constant
Hence, we now have a rotational work-kinetic
energy theorem, except
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Angular Momentum
In linear dynamics, complex interaction
(collisions) can be examined using the
conservation of momentum.
In rotational dynamics, the concept of angular
momentum similarly eases complex interactions.
(Derivation similar to all other rotational quantities)
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Angular Momentum
In linear dynamics:
In rotational dynamics:
Hence, the net torque is equal to the rate of
change of angular momentum. Hence, if there is
no net torque, angular momentum is conserved.
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Angular Momentum
We can change the
angular velocity by
modifying the moment
of inertia.
Angular momentum is
conserved, but where
has the extra energy
come from?
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Angular Momentum
I have to apply a
force on the
mass to change
its linear velocity.
Through NIII, the
mass applies a
force on me.
For every torque there is an equal and opposite retorque.
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Angular Momentum
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Angular Momentum
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Angular Momentum
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Angular Momentum
Consider a lecturer on a
rotating stool holding a
spinning wheel, with
the axis of the wheel
pointing towards the
ceiling.
What happens when the
wheel is turned over?
http://www.physics.lsa.umich.edu/demolab/demo.asp?id=696
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Angular Momentum
As with linear momentum, we
can use conservation of
angular momentum without
having to worry about the
various (internal) torques in
action.
External torques will change
the value of the total angular
momentum.
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Linear & Angular Momentum
What is the angular momentum
of an object moving along a
straight line?
Objects moving linearly have constant angular momentum.
Rotational mechanics is linear mechanics in a different
coordinate system.
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