Problem 4 SAMPLE PROBLEM 15.13 eonsidered, its The bent rod OAB rotates about th

Question

Problem 4 SAMPLE PROBLEM 15.13 eonsidered, its The bent rod OAB rotates about the vertical OB. At the instant rad/s and angular velocity and angular acceleration are, respectively, 20 collar D 200 rad/sa, both clockwise when viewed from the positive Y axis. The veloc- moves along the rod and at the instant considered, OD 8 in., and the ity and acceleration of the collar relative to the rod are, respectively, 50 in./s and 600 in./sa, both upward. Determine (a) the velocity of the collar, (b) the acceleration of the collar. We atta

Explanation / Answer

(a) The velocity of the collar

calcualting this for a instant when the angular velocity is 40 rad/s, For calculation of the absolute velocity, we have to understand that due to clockwise rotation of the link collar will have linear velocity in the outward direction that means for absolute velocity we have to do vector addition of both the velocities.
So the linear velocity due to the angular velocity , Linear velocity = Angular velocity(W)*Radius of circle (R)
Radius of circle = 8Cos30 = 6.928 in
Linear velocity = WR = 40*6.928=277.128 in/s
Absolute velocity = Linear velocity due to rotation + velocity of collar
= 277.128+50 = 327.128 in/s

(b)The accelarationn of the collar

calculating acceleration we have to consider one more term that is coriollis acceleration, that is ac = 2VW
aC= 2*50*40= 400 in/s2 this will act perpendicular to the collar motion that is perpenicular to rod.
aR = rw2 where r is radius of circle that is r= 8Cos30 = 6.928 in , w is angular velocity = 40 rad/s
aR = 11085.125 in/s2 , direction will be perpendiculr to the aC
Now at tangential acceleration = angular acceleration*radius = 400*6.928 = 2771.2 in/s2 direction will be in the aC
and one linear acceleration that is 500 in/s2 is in the direction of the opposite of radial
So the net acceleration in the direction of the aC = 400+2771.2 = 3171.2 in/s2
In perpendicular direction of aC = 11085.2 - 500 = 10585.2 in/s2
Now by applying pythagoras theorem we can calculate the absolute value of the acceleration.

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