Rotational and translational motion

[Kaushik]

Homework Statement

A Uniform rod AB of length 7m is undergoing combined motion such that, at some instant, velocities at top most point A is perpendicular to the rod and magnitude is 11 m/s. The mid point/ centre of mass ,say C, has a velocity of 3 m/s and is also perpendicular to the rod. If both the velocities are in opp. direction. Determine the acceleration of point A and angular velocity of the rod. ( Velocity of the centre C and angular velocity of the rod remains constant.

Relevant Equations

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A Uniform rod AB of length 7m is undergoing combined motion such that, at some instant, velocities at top most point A is perpendicular to the rod and magnitude is 11 m/s. The mid point/ centre of mass ,say C, has a velocity of 3 m/s and is also perpendicular to the rod. If both the velocities are in opposite direction. Determine the acceleration of point A and angular velocity of the rod. ( Velocity of the centre C and angular velocity of the rod remains constant.

Could you please help me out in starting with the problem? HINTS on how to proceed would be appreciated. Thanks!

 

[collinsmark]

Homework Statement: A Uniform rod AB of length 7m is undergoing combined motion such that, at some instant, velocities at top most point A is perpendicular to the rod and magnitude is 11 m/s. The mid point/ centre of mass ,say C, has a velocity of 3 m/s and is also perpendicular to the rod. If both the velocities are in opp. direction. Determine the acceleration of point A and angular velocity of the rod. ( Velocity of the centre C and angular velocity of the rod remains constant.
Homework Equations: .

A Uniform rod AB of length 7m is undergoing combined motion such that, at some instant, velocities at top most point A is perpendicular to the rod and magnitude is 11 m/s. The mid point/ centre of mass ,say C, has a velocity of 3 m/s and is also perpendicular to the rod. If both the velocities are in opposite direction. Determine the acceleration of point A and angular velocity of the rod. ( Velocity of the centre C and angular velocity of the rod remains constant.

Could you please help me out in starting with the problem? HINTS on how to proceed would be appreciated. Thanks!

The first order of business is to draw a free body diagram.

After that, you might want to consider using changing to a new frame of reference.

That last part of the problem statement, "Velocity of the centre C and angular velocity of the rod remains constant," is important. What does that tell you about the acceleration of point C? And similarly, what does that tell you about the angular acceleration, $\alpha$, of the rod?

 

[Kaushik]

What does that tell you about the acceleration of point C? And similarly, what does that tell you about the angular acceleration, $α$, of the rod?

Acceleration of C and angular acceleration of the rod = 0?

 

[collinsmark]

Acceleration of C and angular acceleration of the rod = 0?

Correct. So, how can you simplify this problem (perhaps considering a new frame of reference)?

 

[Kaushik]

perhaps considering a new frame of reference

Centre of mass is the best frame of reference in this case. Isn't?

 

[collinsmark]

Centre of mass is the best frame of reference in this case. Isn't?

It does have advantages here.