A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is in the direction shown, which one of the following options is correct ( and are any highest and lowest points on the wheel, respectively)?
Point moves faster than point .
Both the points and move with equal speed.
Point has zero speed.
Point moves slower than point .
In pure rolling motion, the velocity of any point on the wheel is the vector sum of the translational velocity of the center of mass () and the tangential velocity due to rotation (). For a wheel of radius rolling without slipping, the condition is . At the highest point , the translational velocity and rotational velocity are in the same direction. So, the net speed is . At the lowest point (point of contact with the ground), the translational velocity and rotational velocity are in opposite directions. So, the net speed is . Therefore, point moves with a speed of , while point is instantaneously at rest (speed is zero). Thus, point moves faster than point .
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