What is the angular momentum of a figure skater spinning at 2.9rev/s with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5m , a radius of 15cm , and a mass of 59kg ?

L=I ω= (mr²/2) •2πf= mr²πf

=59•0.15²• π•2.9=12.1 kg•m²/s

To calculate the angular momentum of a figure skater, we can use the formula:

Angular Momentum (L) = Moment of Inertia (I) x Angular Velocity (ω)

Step 1: Calculate the moment of inertia (I) of the figure skater.

The moment of inertia for a uniform cylinder can be calculated using the formula:

I = 1/2 * m * r^2

where:
- I is the moment of inertia
- m is the mass of the cylinder
- r is the radius of the cylinder

In this case, the mass of the figure skater is 59 kg and the radius is 15 cm, which is equal to 0.15 m.

I = 1/2 * 59 kg * (0.15 m)^2
I = 0.66375 kg m^2

Step 2: Calculate the angular momentum (L).

The angular velocity (ω) is given as 2.9 rev/s. To convert it to radians per second, we can use the conversion factor:

1 revolution = 2π radians

So, ω = 2.9 rev/s * 2π radians/1 rev
ω = 18.212 radians/s

L = I * ω
L = 0.66375 kg m^2 * 18.212 radians/s
L ≈ 12.09 kg m^2/s

Therefore, the angular momentum of the figure skater spinning at 2.9 rev/s with arms in close to her body is approximately 12.09 kg m^2/s.

To find the angular momentum of the figure skater, we can use the formula:

Angular momentum = Moment of inertia x Angular velocity

First, let's find the moment of inertia of the figure skater. Since the skater is considered a uniform cylinder, we can use the formula:

Moment of inertia (I) = (1/2) x mass x radius^2

Given:
Mass (m) = 59 kg
Radius (r) = 15 cm = 0.15 m

Plugging in the values into the formula, we have:

I = (1/2) x 59 kg x (0.15 m)^2

Simplifying, we get:

I = 0.66375 kg·m^2

Next, we need to convert the angular velocity from revolutions per second (rev/s) to radians per second (rad/s). Since one revolution is equal to 2π radians, the conversion factor is:

1 rev/s = 2π rad/s

Given:
Angular velocity (ω) = 2.9 rev/s

Converting to rad/s:

ω = 2.9 rev/s x (2π rad/1 rev)

Simplifying, we have:

ω = 18.199 rad/s

Now, we can find the angular momentum using the formula:

Angular momentum = Moment of inertia x Angular velocity

Plugging in the values we calculated:

Angular momentum = 0.66375 kg·m^2 x 18.199 rad/s

Calculating the result:

Angular momentum = 12.082 kg·m^2/s

Therefore, the angular momentum of the figure skater spinning at 2.9 rev/s with arms in close to her body is approximately 12.082 kg·m^2/s.