Two ice skaters hold hands and rotate, making one revolution in 2.4 s. Their masses are 60 kg and 70 kg, and they are separated by 1.5 m. Find the angular momentum of the system about their center of mass.
To find the angular momentum of the system about their center of mass, we need to calculate the individual angular momenta of the two ice skaters and then add them together.
The angular momentum of an object can be calculated as the product of its moment of inertia and its angular velocity. The moment of inertia depends on the mass and the distribution of mass about the axis of rotation.
Let's calculate the angular momentum of the first ice skater (mass 60 kg) first. Assuming the skater is a point mass, the moment of inertia can be approximated as the mass times the square of the distance from the axis of rotation (1.5 m):
Moment of inertia1 = mass1 * distance1^2 = 60 kg * (1.5 m)^2
The angular velocity can be calculated from the time taken to complete one revolution. Since they complete one revolution in 2.4 seconds, the angular velocity is:
Angular velocity1 = 2π / time = 2π / 2.4 s
Now, we can calculate the angular momentum of the first ice skater:
Angular momentum1 = moment of inertia1 * angular velocity1
Next, let's calculate the angular momentum of the second ice skater (mass 70 kg) using the same process.
Moment of inertia2 = mass2 * distance2^2 = 70 kg * (1.5 m)^2
Angular velocity2 = 2π / 2.4 s
Angular momentum2 = moment of inertia2 * angular velocity2
Finally, we can find the total angular momentum of the system by adding the individual angular momenta together:
Total angular momentum = angular momentum1 + angular momentum2
Note: This calculation assumes the ice skaters are fixed in space, and their center of mass is stationary. If the skaters are also moving in space, their velocities need to be taken into account to calculate the total angular momentum.