A wheel rolls without slipping on a horizontal surface. The speed of the particle at the highest point of the rim is 8 m/s. The speed of a particle on the rim that is at the same level as the centre of the wheel is:
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Question

A wheel rolls without slipping on a horizontal surface. The speed of the particle at the highest point of the rim is 8 m/s. The speed of a particle on the rim that is at the same level as the centre of the wheel is:

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G1 Physics · Accepted Answer

For pure rolling, V C M V_CM V C ​ M = Rω. At the highest point, translational and rotational velocities are in the same direction, so v t o p v_top v t ​ o p = V C M V_CM V C ​ M + Rω = 2 V C M . V_CM. V C ​ M . Given v t o p v_top v t ​ o p = 8 m/s: 2 V C M V_CM V C ​ M = 8 ⇒ V C M V_CM V C ​ M = Rω = 4 m/s. At a side point at the same height as the centre, the translational velocity V C M V_CM V C ​ M and the rotational velocity Rω are perpendicular to each other. Therefore, v = √( V C M 2 V…