Question

The centrifuge at NASA Ames Research Center has a radius of 8.8 m and can produce forces on its payload of 20 gs or 20 times the force of gravity on Earth.

What is the angular momentum of a 20-kg payload that experiences 10 gs in the centrifuge?

a) 1760 kg·m²/s
b) 2640 kg·m²/s
c) 3520 kg·m²/s
d) 4400 kg·m²/s

Answer 1

To calculate the angular momentum of a payload experiencing 10 gs in the centrifuge, the linear velocity must first be found using the centripetal acceleration formula and then multiplied by the mass and radius to get the angular momentum.

Step-by-step explanation:

To calculate the angular momentum of the payload, you need to understand that angular momentum (L) can be expressed as L = mvr, where m is mass, v is the linear velocity, and r is the radius of the circular path.

First, let's find the linear velocity (v) using the centripetal acceleration formula, which states that a = v^2 / r, where a is centripetal acceleration. We are given that the payload experiences 10 g's, which is 10 times the acceleration due to gravity (g = 9.8 m/s2), so a = 10 * 9.8 m/s2. Knowing the radius (r) is 8.8 m, we can rearrange the formula to solve for v: v = sqrt(a * r).

After finding v, we can plug the values into the angular momentum formula:

L = m * v * r

We are given that m = 20 kg and r = 8.8 m, so after calculating v, we would multiply all the values to find the angular momentum, which will give us the answer in kg·m2/s.