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A Rod Ab Has an Angular Velocity of 2 Rad/Sec,Counter Clock Wise as Shown.End C of Rod Bc is Free to Move on a Horizontal Surface.Determine: (1)Angular Velocity of Rod Bc (2)Velocity of C - Engineering Mechanics

Answer in Brief

A rod AB has an angular velocity of 2 rad/sec,counter clock wise as shown.End C of rod BC is free to move on a horizontal surface.Determine:
(1)Angular velocity of rod BC
(2)Velocity of C

Given : ωAB=2 rad/sec (anti clockwise)

To find : ωBC
               VC

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Solution

 

BY GEOMETRY :
Assume I to be the ICR of rod BC

In △IAB,

∠BIC=40° 

∠IBC=90°
`tan 40 = (BC)/(IB) = (0.5)/(IB)`

`sin 40 = (BC)/(IC)  = (0.5)/(IC)`
IB = 0.5959m and IC = 0.7779m

vB = rω

     = ABxωAB
     = 0.3 x 2
     = 0.6 m/s

  ωBC = `(v_B)/r`
          `= (v_B)/(IB)`
           `= (0.6)/(0.5959)`
            =1.0069 rad/sec
The direction is anti-clockwise

vC = rω

     = IC x ωBC
     = 0.7779 x 1.0069
     = 0.7832 m/s  
   The direction of vC is towards right

Angular velocity of BC=1.0069 rad/sec(anto clockwise)
vC=0.7832 m/s(Towards right) 

Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
  Is there an error in this question or solution?
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