11) The two ends A and B of a uniform rod of length L = 1 and mass m are - Physics - Systems of Particles and Rotational Motion

Question

11) The two ends A and B of a uniform rod of length L = 1 and mass
m are moving with velocities vA and vB as
shown The angular velocity of the rod is
a )   20   r a d / s b )   25   r a d / s c )
  30   r a d / s d )   50   r a d / s

Sanjay Singh · Accepted Answer

Dear student
Let the line joining A to B be X axis and Y axis is perpendicular to the X axis
Velocity of point A with respect to B along the line joining A and B is zero
Velocity of A along  X axis towards B is VAX=20cos53°=20×35=12m/sVelocity of B along  X axis towards A  is VBX=Vcos37°=V×45m/s12=V×45V=5×124=15m/sAngular velocity of rod is ω=Velocity of point A with respect to B in the direction perpendicular to the line joining A and B Separation between A and BVelocity of A  perpendicular to the line joining A and B is  VAY=20sin53°=20×45=16m/sVelocity of B  perpendicular to the line joining A and B is VBY=15sin37°=15×35=9m/sω=16+91=25rad/sRegards

11) The two ends A and B of a uniform rod of length L = 1 and mass m are moving with velocities vA and vB as shown. The angular velocity of the rod is. a ) 20 r a d / s b ) 25 r a d / s c ) 30 r a d / s d ) 50 r a d / s

11) The two ends A and B of a uniform rod of length L = 1 and mass m are moving with velocities v_A and v_B as shown. The angular velocity of the rod is.
$a) 20 r a d / s b) 25 r a d / s c) 30 r a d / s d) 50 r a d / s$