An ice skater begins to spin, starting with his arms spread out as much as possible, parallel come the ice. He traction his arms into his body, and then raises them completely vertically towards the ceiling. As the ska pulls his arms inward, his angular velocity will certainly __________, and as that raises his eight vertically his angular velocity will __________.

You are watching: As an ice skater begins a spin

Explanation:

Through preservation of angular momentum, as moment of inertia decreases, the angular velocity increases. Minute of inertia is dependence on the distribution of the spinning body"s mass far from the facility of mass—as the skater brings his eight in, he lowers his minute of inertia, therefore increasing his angular velocity. If he raises his arms fully vertically from this point, the does not readjust the radius the mass distributions (from the facility of his body), thus maintaining his angular velocity.

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### Example inquiry #72 : movement

Sarah spins a ball of mass

attached come a string of length
around she head through a velocity
. If the ball splits in half, losing exactly one-half that its mass instantaneously, what is its new velocity,
?

Explanation:

By the preservation of angular momentum, the angular momentum

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

Here,

is the early mass,
is the initial angular velocity, and
is the size of the rope, which stays constant. Angular momentum should be conserved, thus:

Substitute.

We are provided that

and
is the last velocity. Plug in and also solve.

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### Example question #73 : movement

A kid is standing in ~ the facility of a frictionless, rotating platform. Both the child and also the platform room rotating with and initial angular velocity,

. The child starts to walk progressively toward the sheet of the platform. Which quantity will decrease as the son walks?

Total angular inertia

Total angular momentum

Total momentum

Rotational inertia that the disk

Total rotational kinetic energy

Total rotational kinetic energy

Explanation:

Since the platform is frictionless, together the son walks, angular inert is conserved. However, because there is an

term in the kinetic power expression, as
decreased as result of the boost of inertia, that affects the energy more, and it decreases. Indigenous the reference structure of the disk, the kid feels an outside directed force, and also thus is doing an unfavorable work. This is the very same principle that enables ice skaters to rise their spinning speed.

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### Example question #71 : Ap Physics C

Two heavy cylinderical disks have equal radii. The very first disk is rotate clockwise in ~

and the 2nd disk is turn counterclockwise at
. The second disk has actually a mass 3 times larger than the first. If both spinning disks are an unified to type one disk, they end up rotating at the exact same angular velocity and also same direction. Discover this angular velocity ~ combination.

Explanation:

For the first disk, we have actually the details below.

For the second disk, we have actually the info below.

(The minus sign suggests counterclockwise while the positive indicates clockwise.)

To carry out this problem, we use conservation that angular momentum. Before the disks are put in contact, the initial total angular momentum is offered by the equation below.

It is just the sum of the angular momentums of each disk. When the disks are an unified together, then last angular momentum have the right to be uncovered by the adhering to equation.

Set this equal to the early stage angular momentum.

Simplify and also solve for

.

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### Example question #2 : making use of Angular momentum Equations

A item of room debris is travelling in one elliptical orbit around a planet. In ~ its closest allude to the planet, the debris is travelling at

. When the debris is
from the planet, it travels at
. Exactly how close walk the debris acquire to the earth in the orbit?

Explanation:

The equation because that conservation the angular momentum is:

This method that the angular inert of the thing at the 2 points in that is orbit have to be the same. Because the fixed of the debris does no change, this provides us an equality the the product that the velocity and distance the the debris at any two points of its orbit:

Plug in recognized values.

There is disagreement between units; the velocities are given in both

and
. Glance under at the answer choices and note that they room all lengths in kilometers.

Solve for

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### Example question #74 : activity

A mechanic is making use of a wrench to loosen and also tighten screws on an engine block and wants to increase the quantity of torque the puts top top the screws to adjust them an ext easily. I m sorry of the following steps will certainly not aid him to carry out so?

Pulling or pushing at one angle the is much less perpendicular to the wrench

Pulling or advertise at an angle the is an ext perpendicular come the wrench

Using a longer wrench

Using a wrench the a various material

Increasing the magnitude of the force he puts on the wrench

Pulling or advertise at an angle the is much less perpendicular come the wrench

Explanation:

Remember the talk equation:

Exerting pressure on the wrench in ~ an angle much less perpendicular to the wrench will reduce

and also thus alleviate the torque.

The various other answer alternatives will all increase the torque being applied, do the twisting movement easier.

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### Example inquiry #1 : Friction and Normal force

Weightlessness is experienced when the normal force amounts to __________.

zero

a negative value

the force because of gravity

the massive of the object

zero

Explanation:

"Weightlessness" is analogous come free-fall (neglecting waiting resistance), during which the only force on things is the pressure of gravity. Once normal pressure becomes zero, the object loser physical call with the surface.

When normal force is equal to the pressure of gravity, the object is in equilibrium and also the net vertical force is zero. This results in zero acceleration, however does not result in "weightlessness." mass is not a force, and an unfavorable force worths merely show relative direction (assuming correct calculations)

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### Example question #2 : Friction and also Normal pressure

A publication of massive 1kg is organized to a vertical wall by a person"s hand using a 20N force directly toward the wall. The wall has a revolution friction coefficient of 0.3 and also a kinetic friction coefficient that 0.2. With the book held at rest, what the is frictional force keeping the publication from sliding under the wall?

Explanation:

Frictional force is calculated using the typical force and the friction coefficient. Because the publication is at rest (not in motion), we use the coefficient of revolution friction.

The normal pressure will be equal and opposite the force pushing directly into the surface; in this case, that means the normal pressure will be 20N.

See more: All Things Are Possible With Christ Who Strengthens Me, Philippians 4:13 Nkjv

Solve for the force of friction:

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Explanation:

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### Example question #4 : Friction and Normal pressure

Explanation:

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