Compute the velocity of a bar:
A bar AB as shown in Figure slides so that its bottom point A has a velocity of 4 m/sec to the left along the horizontal plane. compute the velocity of B and also the angular velocity ω.
Solution
A bar AB is resting on two surfaces as illustrated in Figure (a). If end A starts moving to the left then B shall start sliding down along the sloping surface as illustrated in Figure (b). To locate instantaneous centres draw perpendiculars to v_{A} at A and to v_{B} at B. These perpendiculars meet at O. Consider Δ AOB.
∠ OAB = 75^{o} , ∠ ABO = 60^{o}
∴ ∠ AOB = 45^{o}
By using sine rule, we can get the length AO and BO.
∴ AB/ sin 45^{o} = AO /sin 60^{o} = BO /sin 75^{o} , where AB = 1000 mm
∴ AO = 1.225 m
BO = 1.366 m
Now, v _{A} = AO ω
∴ ω = v_{A} / AO = 4/1.225 = 3.265 rad / sec
and
v_{B} = OB ω = 3.265 × 1.366 = 4.46 m / sec