At the shown instant, point O is fixed and point A has velocity v horizontally to the right. The horizontal and vertical separations between O and A are each d. If the angular velocity of A with respect to O is xv/(2d), find x.

Question

G1 Physics · Accepted Answer

Take O as the origin. At the instant shown, r⃗(OA)=d î+d ĵ, v⃗(A/O)=v î. The instantaneous angular velocity magnitude of A about O is ω=|r⃗×v⃗|/|r⃗|². Here |r⃗×v⃗|=dv and |r⃗|²=d²+d²=2d². Therefore ω=dv/(2d²)=v/(2d). Comparing with xv/(2d), x=1.