Manually triggered variable speed rotating system
Get a motor with an encoder on it. The encoder allows you to monitor position and velocity (to some extent, you need enough resolution on the encoder for velocity control). Some motor controllers come with feedback from a encoder built in and encoder/motor/controller kits can be found at many motor manufacturers. 

If you have no experience with control systems, a project like this might be a little difficult. Once the globle started spinning after a set time you could monitor the velocity and then give the velocity command to the controller. 

When stopping, if there were a force acting on the globe, it would show up in the velocity error term of the controller (if you have access to it). If it reached a certain threshold (which would indicate there is additional force acting on the motor), you could ramp down the velocity.