A wheel of a bullock cart is rolling on a level road, as shown in the figure below. If its linear speed is v in the direction shown, which one of the following options is correct (P and Q are any highest and lowest points on the wheel, respectively) ?
In rolling motion, a point on a wheel's circumference exhibits both rotational and translational movement. The velocities from these motions combine vectorially.
Phase 2: Examine Velocities at Points P and Q
Point P, located at the wheel's apex, possesses a velocity equal to the wheel's linear speed (v) plus its rotational speed (v).
Point Q, situated at the wheel's base, experiences a linear speed (v) that is counteracted by its rotational speed (-v), resulting in a net zero velocity.
Phase 3: Quantify Velocities
Velocity at P:
$$ v_P = v + v = 2v $$
Velocity at Q:
$$ v_Q = v - v = 0 $$
Phase 4: Synthesis
Point P demonstrates higher velocity compared to Point Q, which is stationary.
