Rotation and Translation Combined. Hockey Stick.

In summary, the hockey stick experiences both translational and rotational motion as it is projected along the ice floor. However, due to the unequal distribution of mass and friction forces along the stick, its rotational and translational motion stop at the same time, as the rotation causes a torque on the center of mass, keeping it in motion until the rotation stops.
  • #1
karansingh
1
0

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.
 
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  • #2
karansingh said:

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
 
  • #3


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.
 

1. What is the difference between rotation and translation?

Rotation is the movement of an object around a fixed point, while translation is the movement of an object from one location to another without any rotation.

2. How are rotation and translation combined in the context of a hockey stick?

In the context of a hockey stick, rotation and translation are combined to describe the movement of the stick as it is swung and moved across the ice. The rotation of the stick allows for a smooth and controlled swing, while the translation allows the stick to move in a specific direction.

3. How does rotation and translation affect the performance of a hockey stick?

The combination of rotation and translation in a hockey stick allows for precise and controlled movements, resulting in more accurate shots and passes. It also allows for quick changes in direction and movements on the ice, making it an essential aspect of a hockey player's performance.

4. Can you explain the physics behind rotation and translation in a hockey stick?

Rotation and translation in a hockey stick are governed by the laws of motion and torque. When the stick is rotated, it creates angular momentum, which helps with the swing and movement of the stick. Translation, on the other hand, is affected by the force and direction of the player's movement, resulting in a change in the stick's position.

5. How can players improve their use of rotation and translation with a hockey stick?

Players can improve their use of rotation and translation with a hockey stick by practicing and developing their coordination and technique. This includes understanding the physics behind these movements and consistently working on their skills through drills and gameplay. Proper training and technique can greatly enhance a player's ability to effectively use rotation and translation in their performance on the ice.

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