PURPOSE: To illustrate the accelerating disc problem.
DESCRIPTION: A mass m is attached to a string hanging over a pulley 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.
REFERENCES: (PIRA unavailable.) See Demonstration Reference File for further information, including sample calculations and data.
EQUIPMENT: Air Table, large disk, small mass with string, level, and timer.
SETUP TIME: 5 min.
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