How Does Angular Momentum Affect a Skater's Spin?

In summary, the conversation focuses on rotational inertia and angular velocity, specifically in relation to a skater and a diver. The initial angular velocity of the skater is 15 rad/s with a rotational inertia of 2.78 kg·m2 when her arms are extended. After pulling her arms in and reducing her rotational inertia to 1.65 kg·m2, her new angular velocity is 25.27 rad/s. The conversation then turns to a diver, where it is stated that the rotational inertia for a pike position is 15.5 kg m2 and 8.0 kg m2 for a tucked position. The question asks how many turns the diver can make when jumping off a 10.0-m
  • #1
mikefitz
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A skater is initially spinning at a rate of 15 rad/s with a rotational inertia of 2.78 kg·m2 when her arms are extended. What is her angular velocity after she pulls her arms in and reduces her rotational inertia to 1.65 kg·m2?

I have so much trouble with these problems because I haven't a clue where to begin. I know that rotational inertia = http://library.thinkquest.org/16600/advanced/5-7.gif.[/URL] Angular velocity is [PLAIN]http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/avel3.gif.[/URL] Knowing this, how can I derive the the new angular velocity?
 
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  • #2
Think about the physical meaning of that situation. What is conserved?

P.S. This is probably the most typical example for the conservation of _______ ________. :smile:
 
  • #3
cool, I got it. 2.78 * 15 = 1.65w

w=25.27 rad/s!

I have one more conservation of momentum...

The rotational inertia for a diver in a pike position is about 15.5 kg m2; it is only 8.0 kg m2 in a tucked position (the figure above).

(a) If the diver gives himself an initial angular momentum of 106 kg m2/s as he jumps off the board, how many turns can he make when jumping off a 10.0-m platform in a tuck position? [Hint: Gravity exerts no torque on the person as he falls; assume he is rotating throughout the 10.0 m dive.]
So, I know that

P=106kg m^2
d=10m
I=8kg m^2I need to find out what w is so that I can convert to revolutions per second and then figure out how many times the guy rotates before he comes in contact with the water, only I don't know how to do this without his mass or radius?
 

FAQ: How Does Angular Momentum Affect a Skater's Spin?

What is angular velocity on a skater?

Angular velocity on a skater refers to the rate at which a skater rotates around a fixed point, such as their foot or the center of a turn. It is measured in radians per second and is a measure of how quickly the skater is spinning.

How is angular velocity calculated on a skater?

Angular velocity on a skater can be calculated by dividing the change in the skater's angular position by the change in time. This can be expressed as ω = Δθ/Δt, where ω is angular velocity, Δθ is change in angular position, and Δt is change in time.

What factors affect a skater's angular velocity?

A skater's angular velocity can be affected by a number of factors, including their body position, the force of their movements, the surface they are skating on, and any external forces acting on them. For example, a skater can increase their angular velocity by pulling their arms and legs in closer to their body, or by pushing off the ground with more force.

How does angular velocity impact a skater's performance?

Angular velocity plays a crucial role in a skater's performance, as it determines how quickly they can complete spins and turns. A higher angular velocity allows a skater to execute faster and more complex movements, while a lower angular velocity may limit their abilities and make it more difficult to perform certain tricks or routines.

Can angular velocity be controlled by a skater?

Yes, a skater can control their angular velocity by adjusting their body position and the force of their movements. By understanding the relationship between their body, the surface they are skating on, and external forces, a skater can manipulate their angular velocity to perform various spins and turns with precision and control.

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