Dynamics | Part IA, 2006

A car is at rest on a horizontal surface. The engine is switched on and suddenly sets the wheels spinning at a constant angular velocity Ω\Omega. The wheels have radius rr and the coefficient of friction between the ground and the surface of the wheels is μ\mu. Calculate the time TT when the wheels start rolling without slipping. If the car is started on an upward slope in a similar manner, explain whether TT is increased or decreased relative to the case where the car starts on a horizontal surface.

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