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Rotational dynamics



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Physics    Newtonian Mechanics    Rotational dynamics

Non equilibrium Applications of Newton’s Laws for Rotation:

There are some cases where the conditions of equilibrium not satisfied. However, we can apply
Newton’s laws. Let us consider such a case where we have two masses m1 and m2 tied with a
string and a wheel as shown in the figure. Now the whole system has an angular momentum:




Then the total external torque can be expressed as the
rate of change of angular momentum:




However, we have the rate of change of velocity as the acceleration and thus we can write the
acceleration of the system as:



This treatment gives the idea about a non-equilibrium system where Newton’s laws can be
applied to obtain the acceleration of the system.

Combined Rotational and Translational Motion:

The expression for rotational kinetic energy (T) of a rigid body or a system of masses is given as follows:



The translational kinetic energy of a body with constant mass m, with its center of mass moving in a straight line with speed v, is equal to



So the combined kinetic energy for a system experiencing both rotational and translational motion
is given by the formula:

E = Et + T = ½ mv2+ ½ I ω2


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