Rotational and translational motion

In summary, a uniform rod AB of length 7m is undergoing combined motion with velocities of 11 m/s at the topmost point A and 3 m/s at the midpoint/centre of mass C, both perpendicular to the rod and in opposite directions. With the velocity of point C and angular velocity of the rod remaining constant, the acceleration of point A and angular velocity of the rod can be determined. By considering the centre of mass as the frame of reference and taking into account that the velocity of point C and angular velocity of the rod are constant, it can be simplified to show that the acceleration of point C and angular acceleration of the rod are both zero.
  • #1
Kaushik
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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!
 
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  • #2
Kaushik said:
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, [itex] \alpha [/itex], of the rod?
 
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  • #3
collinsmark said:
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?
 
  • #4
Kaushik said:
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)?
 
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  • #5
collinsmark said:
perhaps considering a new frame of reference
Centre of mass is the best frame of reference in this case. Isn't?
 
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  • #6
Kaushik said:
Centre of mass is the best frame of reference in this case. Isn't?
It does have advantages here. :wink:
 
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1. What is the difference between rotational and translational motion?

Rotational motion refers to movement around an axis or center point, while translational motion refers to movement in a straight line. In rotational motion, an object maintains a constant distance from the axis of rotation, while in translational motion, an object's distance from the starting point changes.

2. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around an axis. It is typically measured in radians per second (rad/s) and can be calculated by dividing the change in angular displacement by the change in time.

3. How does torque affect rotational motion?

Torque is a force that causes an object to rotate around an axis. It is directly proportional to the angular acceleration of the object, meaning that a greater torque will result in a faster rotation. Torque is also affected by the distance between the force and the axis of rotation, with a longer distance resulting in a greater torque.

4. What is the relationship between linear and angular momentum?

Linear momentum refers to an object's motion in a straight line, while angular momentum refers to an object's rotational motion. The two are related by the moment of inertia, which is a measure of an object's resistance to rotational motion. The higher the moment of inertia, the more difficult it is to change an object's angular momentum.

5. How do you calculate the center of mass for a rotating object?

The center of mass for a rotating object can be calculated by finding the weighted average of the positions of all the particles that make up the object. This can be done by dividing the sum of the mass of each particle multiplied by its distance from the axis of rotation by the total mass of the object. The resulting center of mass is the point around which the object will rotate.

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