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Astronauts need to be trained to endure the large accelerations sustained during rocket launches. To do this, an astronaut can be placed inside a drum rotating about its vertical axis. A) Suppose that the astronaut is at a distance R from the axis. How many times per second must the drum rotate if the magnitude of the centripetal acceleration of the astronaut is 8g. Express your answer in terms of R and g.

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Explanation:

Formula for calculating centripetal acceleration a = v²/r

For us to know how many times per second must the drum rotate if the magnitude of the centripetal acceleration of the astronaut is 8g is similar to calculating the velocity of the drum.

Next is for us to make v the subject of the formula.

a = v²/r

v² = ar

v = √ar

From the question we are given:

a = 8g

Since the astronaut is at a distance R, then r = R

Substitute the given parameters into the formula v = √ar

v = √8g×R

v = √8gR

v = √8 × √gR

v = √8 × g

v = √(4×2) × √gR

v = 2√(2gR)

Hence the drum will rotate at 2√(2gR) m/s

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