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