Physics for Geologists, Second edition

20 Force
Figure 2.3 Torque is the product of mass and the distance from the axis of
rotation. The system illustrated is static and in balance.
newton metres (Nm). A large force acting on a short lever does the same
work as a small force on a long lever (Figure 2.3). This is how you lift a car
with a jack, and how some weighing scales work. You can tighten a nut more
easily with a longer spanner. The moment of inertia is a measure of resistance
to angular acceleration and again, it is a passive property of a revolving
system [ML~]. Angular momentum, or the moment of momentum, is the
product of the momentum and the length of the radius of rotation [ML~T-~],
in units of kg m2 sP1.
Why does a spinning skater spin faster when her arms are brought closer to
the body? The conservation of momentum, in this case angular momentum,
means that if you reduce the moment (the radius of rotation) you increase
the speed of rotation. The same is true of the Earth-Moon system.
Potential energy
Gravitational potential energy is energy due to position -energy that can be
realized by letting the body fall. Fill a hand-basin with water, and the water
has potential energy that can be realized by taking out the plug. The water
can then do work as it descends to a lower level. Surplus electric energy is
used to pump water from the Wivenhoe dam in Queensland, Australia, to
the higher Splityard Creek dam: its potential energy in the Splityard Creek
dam means that electricity can be generated at peak periods by letting the
water flow back into the Wivenhoe dam through the hydroelectric plant.
Potential energy is relative to some datum.
A body of mass m at height h above the ground has potential energy
relative to the ground of mgh N m because that is the amount of work it could
do in falling a vertical distance h to the ground in a frictionless process - or
the amount of work needed to raise it to height h above the ground. In reality,
some of the energy is invariably lost by friction to heat. The Full Supply Level
of Splityard Creek dam is about 100 m above that of Wivenhoe dam, so the
potential energy of the water behind the Splityard Creek dam relative to the
water behind the Wivenhoe dam is nearly lo6 N m, or 1 MN m or 1 MJ or
1 MW s per cubic metre.
There is another mechanical potential energy - elastic, as in an old-
fashioned clock.
Copyright 2002 by Richard E. Chapman