**Mastering Physics: Hockey Stick and Puck**

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## Question “Mastering Physics: Hockey Stick and Puck”

A hockey stick of mass m_{s} and length L is at rest on the ice (which is assumed to be frictionless). A puck with mass m_{p} hits the stick a distance D from the middle of the stick. Before the collision, the puck was moving with speed v_{0} in a direction perpendicular to the stick, as indicated in the figure. The collision is completely inelastic, and the puck remains attached to the stick after the collision.

Find the speed v_{f} of the center of mass of the stick+puckcombination after the collision. Express v_{f} in terms of the following quantities: v_{0}, m_{p}, m_{s}, and L.v_{f} =

After the collision, the stick and puck will rotate about their combined center of mass. How far is this center of mass from the point at which the puck struck? In the figure, this distance is (D-b) . (D-b) =

What is the angular momentum L_{cm }of the system *before the collision*, *with respect to the center of mass of the final system*? Express L_{cm }in terms of the given variables.L_{cm} =

What is the angular velocity w of the stick+puckcombinationafter the collision? Assume that the stick is uniform and has a moment of inertia i_{0} about its center. Your answer for w should not contain the variable b.

w = |

Which of the following statements are TRUE?

1) Kinetic energy is conserved.

2) Linear momentum is conserved.

3) Angular momentum of the stick+puck is conserved about the center of mass of the combined system.

4) Angular momentum of the stick+puck is conserved about the(stationary) point where the collision occurs.

## Answer

Concepts and Reason

This problem can be solved using the following concepts: the law of conservation and momentum, the center mass, angular acceleration, a moment inertia, and conservation angular momentum.

In the first instance, use the law of conservation and momentum to substitute mass and velocity before and during the collision. Next calculate the speed at which the puck and stick combination will be moving after the collision.

Next, calculate the distance between the center mass of the point where the puck struck. Before the collision, the stick is concentrated at *D*. *Db* is the distance from the point at which the puck strikes the stick.

Next, calculate the angular momentum for the puck relative to the system’s center of mass. You can substitute mass and velocity for the distance from the point at which the puck touches the stick *Db*.

Next calculate the moment of equilibrium of the puck and stick around the center of mass. Next calculate the initial and final angular momentum. Finally, use the conservation of momentum to calculate the angular velocity for the stick-puck combination after collision.

Find the truth or false of the statement, and then give the correct information or hint as to the incorrect statement.

Fundamentals

The law of conservation of angular momentum for stick-puck combination is

mpv0 = (mp+ms)vf

Here, m = the mass of a puck and m = the mass of a stick. v _{0} indicates the initial velocity of a puck and v _{f} the final speed of the stick-puck combination.

The stick’s center mass is located at

*b* represents the center of mass, and *D* the distance from it.

The moment of inertia is the position of the stick around the center of mass.

Here, I _{} represents the moment of inertia for the stick, and I _{} the initial moment.

The moment of inertia is the puck’s movement around the center of mass.

Here, I _{and p} are the moments of inertia for the puck. D-b refers to the distance between the center of mass and the puck.

The puck’s initial angular momentum relative to the center mass of the system is

L cm represents the initial angular momentum for the puck relative to the center mass.

The total moment inertia for the puck and stick is

*I* here is the total moment inertia.

The final angular momentum,

Here L _{f} represents the system’s final angular momentum, and w the angular velocity after collision of the tick-puck combination.

The initial angular momentum is.

Here L _{i} are the initial angular momentum for the system

According to the conservation angular momentum,

L_{f}=L_{i}

(1)

The law of conservation in angular momentum for stick-puck combination is

The expression can be rewritten in terms of v _{or f}.

(2)

The center mass of the puck and stick combination is

The distance between the point at which the puck touches the stick and the center of mass is D-b.

to *b*.

(3)

The puck’s initial angular momentum relative to the system’s center of mass is

Substitute Dm _{for s}/m _{or s}+m .

(4)

The moment of inertia is the position of the stick around the center of mass.

to get b to find I _{and s}.

The moment of inertia is the puck’s movement around the center of mass.

to get D-b to locate I _{and p}.

The total moment inertia for the puck and stick is

To find I, substitute

with

or

with

.

…… (1)

The initial angular momentum is.

to get D-b’s L _{i}.

…… (2)

The final angular momentum,

…… (3)

According to the conservation angular momentum,

In the expression above, use equations (2) and (3).

To find w, substitute equation (1) from the expression above.

(5)

Conserve kinetic energy

This is because the kinetic energy is being transferred from one place into another.

Linear momentum is preserved.

The center of mass of the combined system is where the puck and stick have their angular momentum.

The point at which the collision occurs is the stationary point that the puck and stick retain their angular momentum.

These statements are true since there are no external torque acts. The angular momentum at all points is conserved. We consider the center mass of the entire system to be the linear motion of center mass of new system and the rotation around center mass of new system.

## Conclusion

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