Gear C is meshed with stationary/fixed gear D and can rotate around point A. Gea

Question

Gear C is meshed with stationary/fixed gear D and can rotate around point A. Gear C has a mass of 3 kg and a centroidal radius of gyration of 75 mm. The uniform bar AB has a mass of 2.5 kg. If the system is released from the position shown, determine the velocity [m/s] of point B after bas AB has rotated through 90o . System parameters LAB=200 mm, r=100 mm.

What is the velocity [m/s] of point B after bas AB has rotated through 90 degrees?

idal radius of gyration of 75 mm. The uniform bar AB has a mass sod from the position shown, determine the velocity [m/s] of point h 90°. System parameters LAR200 mm, r-100 mm. the velocity [issof point B after bas AB as td through 90r

Explanation / Answer

Using Conservation of Energy we can say that Potential Energy lost by bar AB and Gear C is equal Kinetic energy gained when they are rotated by 90 degrees

Potential Energy lost = (mAB *g* LAB/2) + (mC *g*LAB)

Substituting the values we get  Potential Energy lost = 8.33 J

Now KInetic energy at final postion = (IAB*wAB2)/2 + (mC * vB2)/2 +(IC* w2C)/2

where IAB and IC are the respective moments of inertia and wAB ,wC are angular velocities

But wC = VB / r and wAB = vB/ LAB

Now, equating Both the equations and solving for vB

v2B = 16.66 /( 0.833 + 3 + 1.40)

v2B = 3.18

vB = 1.784 m/s

Therefore Velocity [m/s] of point B after bas AB has rotated through 90 degrees is 1.784 m/s

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