# Figure skater spinning (rate of rotation)

• kbyws37
In summary, using the principle of conservation of angular momentum, we can calculate the new rate of rotation for a figure skater who reduces her rotational inertia to 68% of its original value. The new rate of rotation is 2.06 rev/s.
kbyws37
A figure skater is spinning at a rate of 1.40 rev/s with her arms outstretched. She then draws her arms into her chest, reducing her rotational inertia to 68.0% of its original value. What is her new rate of rotation?

I am having trouble starting this problem.
I know that
(I)(alpha) = (I)(omega)(t)

however, the problem doesn't mention time..

What physical quantity is conserved in this problem?

Angular momentum is conserved.
So...
(I1)(omega1) = (I2)(omega2)
however i am confused as to how to find omega when i do not have time

Where do you see time mentioned in that equation? What makes you think you need it? (It doesn't matter how fast or how slowly the skater pulls her arms in, since all you care about is the end result.)

sorry i am struggling in physics so i don't really understand.

so
if she reduces her inertia by 68% of its original value...
it would be 0.68*omega

I don't know where to start

kbyws37 said:
so
if she reduces her inertia by 68% of its original value...
Express that mathematically. If her original rotational inertia is I1, what's I2? Note that the precise instructions were:
reducing her rotational inertia to 68.0% of its original value​
That's "to", not "by".

ok thanks. i got it

1.40 rev/s = (0.68)I2
= 2.06 rev/s

Good! I'll rewrite it more systematically.
Conservation of angular momentum says:
(I1)(omega1) = (I2)(omega2)

Given:
omega1 = 1.4 rev/s
I2 = 0.68 I1

So:
(I1)(1.40 rev/s) = (0.68 I1)(omega2)
(1.40 rev/s) = (0.68)(omega2)
omega2 = (1.40 rev/s)/(0.68)

## What is the rate of rotation for a figure skater spinning?

The rate of rotation for a figure skater spinning is typically measured in revolutions per minute (RPM). This can vary depending on the skater's speed and technique, but the average rate of rotation is between 2-3 RPM.

## How does a figure skater achieve a faster rate of rotation?

A figure skater can achieve a faster rate of rotation by pulling their arms and legs closer to their body, which decreases their moment of inertia and allows them to spin faster. They can also increase their rotational speed by pushing off the ice with their skates and using their body weight to generate momentum.

## What factors affect a figure skater's rate of rotation?

There are several factors that can affect a figure skater's rate of rotation, including their body position, speed, and technique. The type of ice surface, temperature, and humidity can also have an impact on the skater's spin.

## Can a figure skater control their rate of rotation?

Yes, a figure skater can control their rate of rotation through various techniques and adjustments. By changing their body position, pushing off the ice with different levels of force, and altering their center of gravity, a skater can increase or decrease their rate of rotation.

## Is there a maximum rate of rotation for a figure skater?

There is no set maximum rate of rotation for a figure skater. However, the International Skating Union (ISU) sets a maximum time limit for spins in competitions, which is typically around 8-10 revolutions. This ensures that the skaters do not become too dizzy or disoriented during their performance.

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