Hi I am using a dc motor for rotary to linear conversion mechanism. DC motor has a torque of 16mNm and speed of 8000 rpm. Please, if anybody know, tell me equations to calculate the time motor shaft takes to completely stop or number of revolutions motor rotates after input voltage is zero. If possible refer to some literature or website. I need high speed motor so i cannot use high torque motor. Best Regards

The general answer to your very non specific question is F=ma. Identify all forces acting on the motor armature and integrate twice. Actually the equation should be in rotational coordinates T= I*(alpha).

This would be highly dependent on any external loads and the internal friction of the motor. I imagine that any calculation would be difficult and highly subject to uncertainty, especially if the external loads are low. The best way would just be to measure it directly.