Project ForgeTheory of Machines
Kinematics of Mechanisms
GATE 2015
Medium
A wheel of radius r rolls without slipping on a horizontal surface. P is the center of the wheel and Q is the point at the top of the wheel (diametrically opposite the contact point). If the velocity of point P is 10 m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is __________.
20 m/s(± 1 accepted)
Explanation
For rolling without slipping, the contact point is the instantaneous center (IC). The center P is at distance r from the IC, moving at 10 m/s. Point Q (top) is at distance 2r from the IC, so its speed is proportional: v_Q = v_P×(2r/r) = 2×10 = 20 m/s.
Source: GATE ME 2015 (Session 1) (2015)
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