What is the angular momentum of a figure skater spinning at 4.4 with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.6 , a radius of 15 , and a mass of 53 ?
To calculate the angular momentum of the figure skater, we can use the formula:
Angular Momentum (L) = Moment of Inertia (I) * Angular Velocity (ω)
First, let's find the moment of inertia of the figure skater. Since the skater is assumed to be a uniform cylinder, the moment of inertia can be calculated using the formula:
Moment of Inertia (I) = (1/2) * mass * radius^2
Given that the radius (r) is 15 cm and the mass (m) is 53 kg, we can substitute these values into the formula:
I = (1/2) * 53 kg * (15 cm)^2
To make the units consistent, we need to convert the radius from centimeters to meters:
I = (1/2) * 53 kg * (0.15 m)^2
Next, we can calculate the moment of inertia:
I = (1/2) * 53 kg * 0.0225 m^2
I = 0.56175 kg•m^2
Now that we have the moment of inertia, we can calculate the angular momentum by multiplying it by the angular velocity. Given that the angular velocity (ω) is 4.4 rad/s:
L = 0.56175 kg•m^2 * 4.4 rad/s
Now, let's calculate L:
L = 2.4693 kg•m^2/s
Therefore, the angular momentum of the figure skater spinning at 4.4 rad/s with her arms close to her body is approximately 2.4693 kg•m^2/s.