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Any mass in motion remains in constant uniform motion (constant speed and direction) unless acted upon by an external force. At any instant in time, the mud particle is moving tangentially on the wheel. If the adhesion between the wheel and the mud is strong enough to transmit a force to the mud and cause it to alter its direction of motion, then its direction of motion will change to follow the wheel. If the mud isn't stuck to the wheel tight enough to transmit the required force, then its direction of motion will not change enough to follow the wheel and it will separate. At the instant of separation, the force goes away, and the mud continues in straight-line motion.

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