A small particle of mass m and its retaining cord is spinning with angular velocity ω on the horizontal surface of a smooth disc. As force F is slightly relaxed, r increases and ω changes. Determine the rate of change of ω with respect to r

Step-by-step solution

During the motion of the object, there is only one force tension which is acting towards a fixed point (centre of the table - disc). So that motion is under the effect to central force and thus, angular momentum will be conserved. At any radial distance, r is L = mωr 2 dL dr = mr 2 dω dr + mω 2 r = 0 So, dω dr =   - 2 ω r