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Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can subsequently interact with any charged particles. EM waves carry energy, momentum and angular momentum away from their source particle and can impart those quantities to matter with which they interact.
Electromagnetic waves travel in a vacuum whereas mechanical waves do not. The mechanical waves need a medium like water, air, or anything for it to travel. The ripples made in a pool of water after a stone is thrown in the middle are an example of mechanical waves.