Yes, ground the motor.
The main reason why grounding is used in electrical distribution network is the safety: when all metallic parts in electrical equipment are grounded then if the insulation inside the equipment fails there are no dangerous voltages present in the equipment case. Then the live wire touches the grounded case then the circuit is effectively shorted and fuse will immediately blow. When the fuse is blown then the dangerous voltages are cut.
To a small child, the perfect granddad is unafraid of big dogs and fierce storms but absolutely terrified of the word “boo.” – Robert Brault