What is the linear velocity in m/s of an astronaut spinning 25.9 RPM (revolutions per minute) in a centrifuge that has a radius of 12 meters?
To calculate the linear velocity of the astronaut, we need to convert the RPM to radians per second and then use the formula for linear velocity in circular motion.
1. First, convert 25.9 RPM to radians per second:
1 revolution = 2π radians
25.9 RPM = 25.9 * 2π radians per minute
25.9 RPM = 25.9 * 2π / 60 radians per second
25.9 RPM = 2.707 radians per second
2. Then, calculate the linear velocity using the formula:
Linear velocity = radius * angular velocity
Linear velocity = 12 meters * 2.707 radians per second
Linear velocity = 32.484 m/s
Therefore, the linear velocity of the astronaut spinning at 25.9 RPM in a centrifuge with a radius of 12 meters is 32.484 m/s.