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.