Rotation and Translation Combined. Hockey Stick.

[karansingh]

Homework Statement

A hockey stick is projected along ice floor such that it possesses rotation about its center of mass as well as translation of it center of mass. Due to friction present, its translation comes to a stop after some time. Why is it that both translational and rotational motion stop together, not before or after each other?

2. The attempt at a solution
One thing i cud come up with that it does not probably hold for regular objects. So as the stick is not uniform, Center of mass, has unequal mass on both side, implying that friction on both sides is different, so as long as the the stick rotates, its center of mass must move as forces are not balanced. Am i Correct?

If not, please suggest the correct solution.

 

[Andrew Mason]

Homework Statement

A hockey stick is projected along ice floor such that it possesses rotation about its center of mass as well as translation of it center of mass. Due to friction present, its translation comes to a stop after some time. Why is it that both translational and rotational motion stop together, not before or after each other?

2. The attempt at a solution
One thing i cud come up with that it does not probably hold for regular objects. So as the stick is not uniform, Center of mass, has unequal mass on both side, implying that friction on both sides is different, so as long as the the stick rotates, its center of mass must move as forces are not balanced. Am i Correct?

If not, please suggest the correct solution.

I think you are right. The friction force is not uniform along the length of the hockey stick. Since friction forces are not equal along the stick, there is a torque on the centre of mass of the stick so long as the stick is rotating. This means that the centre of mass will continue to move until it stops rotating.

AM

 

[kerimek]

Your explanation is partially correct. The unequal mass distribution on the hockey stick does contribute to the combined motion of rotation and translation. However, the main reason for both translational and rotational motion stopping together is due to the principle of conservation of energy.

When the hockey stick is initially projected, both translational and rotational kinetic energies are present. As the stick moves, friction acts on it, converting some of its kinetic energy into heat and slowing down its motion. This decrease in kinetic energy affects both the translational and rotational components, causing them to decrease at the same rate.

If the rotational motion were to stop before the translational motion, it would violate the conservation of energy as some of the initial kinetic energy would have been lost without being accounted for. Similarly, if the translational motion were to stop before the rotational motion, there would be an excess of kinetic energy that would need to be accounted for.

Therefore, it is only when both translational and rotational motion stop together that the conservation of energy is satisfied. This is why the hockey stick comes to a complete stop with both motion components ceasing simultaneously.