A mass m is attached to a string hanging over a
pulley (to left of post) and wound around a disk of mass M and radius
R. This provides a force F = mg and a torque T = mgR, creating both
linear acceleration a=F/M and angular acceleration a=T/I of the
disk, where the moment of inertia of the disk I=MR^2/2, assuming that m
is much smaller than M. The distance d and the rotation Q which
the disk undergoes when released from rest can then be
calculated: d=at^2/2=mgt^2/2M and
Q=at^2/2=mgt^2/MR. Eliminating t, we obtain the
relation between the linear and angular acceleration of the disc, which
can easily be experimentally verified: Q=2d/R.
Note: The air table is only available in rooms 1410,
1412, and 0405 because it will not fit through a standard door.