AP PHYSICS C ANGULAR MOMENTUM FRQ

AP Physics C: Mechanics Help » Mechanics Exam » Motion » Circular and also Rotational Motion » Rotational Motion and Torque » Understanding Conservation of Angular Momentum

A computer mouse sits at the edge of a 

*
diameter record, rotating on a turntable at fifteenager revolutions per minute. If the mouse walks directly inwards to a point 
*
from the center, what will certainly be its new angular velocity? Assume the mass of the record is negligible.

You watching: Ap physics c angular momentum frq


*


*


*


*


*


Explanation:

Relevant equations:

*

*

Write an expression for the initial angular momentum.

*

Write an expression for the last angular momentum.

*

Apply conservation of angular momentum, setting these 2 expressions equal to one another.

*

Solve for the final angular velocity.

*


An ice skater begins to spin, starting via his arms spreview out as far as possible, parallel to the ice. He pulls his arms right into his body, and also then raises them completely vertically towards the ceiling. As the skater pulls his arms inward, his angular velocity will certainly __________, and also as he raises his arms vertically his angular velocity will __________.

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Explanation:

Thunstable conservation of angular momentum, as moment of inertia decreases, the angular velocity rises. Moment of inertia is dependent on the distribution of the spinning body"s mass ameans from the center of mass—as the skater brings his arms in, he lowers his moment of inertia, therefore boosting his angular velocity. If he raises his arms totally vertically from this suggest, it does not change the radius of mass distributions (from the facility of his body), therefore preserving his angular velocity.


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Example Inquiry #1 : Understanding Conservation Of Angular Momentum


Sarah spins a ball of mass 

*
 attached to a string of length 
*
 about her head via a velocity 
*
. If the sphere splits in half, losing specifically one-fifty percent of its mass instantaneously, what is its new velocity,
*
?


Possible Answers:

*
 (no adjust in velocity)


Correct answer:

*


Explanation:

By the conservation of angular momentum, the angular momentum 

*
, is equal to the product of the mass, angular velocity, and also radius (or size of the rope in this case). The equation relating these terms is:

*

Here, 

*
 is the initial mass, 
*
 is the initial angular velocity, and 
*
 is the length of the rope, which continues to be consistent. Angular momentum should be conserved, thus: 

*

Substitute.

*

We are given that 

*
 and 
*
 is the final velocity. Plug in and also solve.

*

*


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Example Inquiry #21 : Rotational Motion And Torque


A son is standing at the facility of a frictionless, rotating platcreate. Both the son and also the platdevelop are rotating through and also initial angular velocity, 

*
. The son begins to walk slowly toward the edge of the platform. Which quantity will decrease as the kid walks?


Possible Answers:

Rotational inertia of the disk


Total angular momentum


Total angular inertia


Total rotational kinetic energy


Total momentum


Correct answer:

Total rotational kinetic energy


Explanation:

Because the platform is frictionless, as the kid walks, angular momentum is conoffered. However, considering that tbelow is an 

*
 term in the kinetic power expression, as 
*
 decreased as a result of the boost of inertia, it affects the power more, and also it decreases. From the reference structure of the disk, the kid feels an external directed pressure, and also hence is doing negative work-related. This is the exact same principle that enables ice skaters to increase their spinning speed.


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