with time. This means that the mass of the body does not change, the body remains rigid and also the axis does not change its position with respect to the body. Since /d , t we get d t ω α = Equating rates of work done and of increase in kinetic energy, τω ω α ( . ) Eq.
( . ) is similar to Newton’s second law for linear motion expressed symbolically as F = ma Just as force produces acceleration, torque produces angular acceleration in a body. The angular acceleration is directly proportional to the applied torque and is inversely proportional to the moment of inertia of the body. In this respect, Eq.( .
) can be called Newton’s second law for rotational motion about a fixed axis. Example . A cord of negligible mass is wound round the rim of a fly wheel of mass kg and radius cm. A steady pull of N is applied on the cord as shown in Fig.
. . The flywheel is mounted on a horizontal axle with frictionless bearings. (a) Compute the angular acceleration of the wheel.
(b) Find the work done by the pull, when 2m of the cord is unwound. (c) Find also the kinetic energy of the wheel at this point. Assume that the wheel starts from rest. (d) Compare answers to parts (b) and (c).
Answer Fig. . (a) We use