Question

NASA explores artificial gravity as a way to counter the physiologic effects of extended weightlessness for future space exploration. NASA's centrifuge has a 58 -foot-diameter arm.

If two humans are on opposite (red and blue) ends of the centrifuge and they rotate one full rotation every second, what is their linear speed in feet per second?

Answer 1

The linear speed of the two humans on opposite ends of the centrifuge is 58π feet per second, or approximately 182.14 feet per second.

Step-by-step explanation:

To calculate the linear speed of the point on the centrifuge, we need to first determine the circumference of the centrifuge's arm. The circumference can be found using the formula C = 2πr, where r is the radius of the centrifuge. Since the diameter of the centrifuge is given to be 58 feet, the radius is half of that, which is 29 feet. Plugging in this value into the formula, we get C = 2π(29) = 58π feet.

Since the two humans rotate one full rotation every second, and there are 2π radians in a full rotation, their angular velocity is 2π radians per second. The linear speed can be found using the formula v = rω, where ω is the angular velocity and r is the radius of the circular path. Plugging in the values, we get v = (29)(2π) = 58π feet per second.

So, the linear speed of the two humans on opposite ends of the centrifuge is 58π feet per second, or approximately 182.14 feet per second.