A wheel is rolling without slipping on a horizontal surface. In an inertial frame of reference in which the surface is at rest, is there any point on the wheel that has a velocity that is purely vertical? Is there any point that has a horizontal velocity component opposite to the velocity of the center of mass? Explain. Do your answers change if the wheel is slipping as it rolls? Why or why not?
Solution 16DQ Step 1 of 3 : The best example for the combined translation and rotation motion is rolling without slipping, as shown in the figure below. As the wheel is symmetrical, its center of mass is at its geometric center. We shall consider the motion in an inertial frame of reference in which the surface on which the wheel rolls is at rest. Step 2 of 3: In such a inertial frame , where there is no slipping while rolling, it should satisfy the following condition. That is the point on the wheel that contacts the surface must be instantaneously at rest so it does not slip. Hence the velocity of the point of contact relative to the center of mass must have the same magnitude but opposite direction as the center-of-mass velocity If the radius of the wheel is R and its angular speed about the center of mass is then the magnitude of is V cm = R