The crack OQ rotates clockwise at 310 RPM. Crank length =10cm, connecting rod length = 50 cm. Also find the velocity of P & angular velocity of rod at that instant

The ICR can be located as follow:

i) draw a perpendicular to the line of action of P

ii) extend OQ to meet the perpendicular.

iii) The intersection gives ICR

In ∆OPQ, by sine rule

$50 / \sin 60 = 10 / \sin θ \\ Θ = 10$

From the figure,

$\ltPIQ = 30 ; \ltIPQ= 80 ; \ltPQI = 70 $

From ∆IPQ, by sine rule

$IP / \sin70 = IQ/ \sin80 = 50/ \sin30 \\ IP = 94cm \\ IQ = 98.5cm \\ W1= 2πN/60 \\ = 2π \times 310/60 \\ = 32.5 rad/s \\ Vq = OQ \times W1 = 10 \times 32.5 = 325 cm/s $

Also, $Vq = IQ \times W2 \\ 325 = 98.5 \times w2 $

$W2 = 3.3 rad/s$ (anticlockwise)

(angular velocity of the connecting rod)

$Vp = IP \times w2 \\ = 94 \times 3.3 = 310.2 cm/s →$