Slider A moves in the horizontal slot with a constant speed v = 1.90 m/s for a s

Question

Slider A moves in the horizontal slot with a constant speed v = 1.90 m/s for a short interval of motion. Determine the angular velocity %u03C9 of bar AB if the displacement xA = 90 mm, and the length L = 440 mm. The angular velocity is positive if counterclockwise, negative if clockwise.

at 63 degrees

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Slider A moves in the horizontal slot with a constant speed v = 1.90 m/s for a short interval of motion. Determine the angular velocity %u03C9 of bar AB if the displacement xA = 90 mm, and the length L = 440 mm. The angular velocity is positive if counterclockwise, negative if clockwise. at 63 degrees

Explanation / Answer

by sine rule

L/sin63 = Xa/sin(gamma)..........................1

L*sin(gamma) = 0.891 Xa

differenticate on both sides wrt to t,

Lcos(gamma)*d(gamma)/dt = 0.891 *dXa/dt

d(gamma)/dt = Wr and dXa/dt = v

Wr = 0.891 *v/(L*cos(gamma)).............2

from 1 we have

sin(gamma) = 0.891*Xa/L

so,

cos(gamma) = sqrt(1-sin^2(gamma))

=sqrt(1-(0.891*Xa/L)^2)

from 2

Wr = (0.891 *v)/(L*sqrt(1-(0.891*Xa/L)^2)

substitute all values given

Wr = (0.891 * 1.90)/(440*10^-3 *sqrt(1-(0.891*90*10^-3/440*10^-3)^2)

Wr = 3.913 rad/s

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