Question

An astronaut is tested in a centrifuge with radius 10 m and rotating according to 0=0.30t². At t = 50 s, what are the magnitudes of the angular velocity

Answer 1

The magnitude of the angular velocity of an astronaut in a centrifuge that rotates according to θ=0.30t² at t = 50 s is 30 rad/s, calculated by differentiating the angular displacement with respect to time and substituting the given time into the resulting equation.

Step-by-step explanation:

The question asks about the magnitude of the angular velocity of an astronaut in a centrifuge at a specific time, given that the centrifuge rotates according to θ=0.30t², where θ is the angular displacement in radians and t is the time in seconds. To find the angular velocity (ω), we need to take the derivative of the angular displacement function with respect to time.

To find the angular velocity at t = 50 s, we differentiate the given function:

dθ/dt = d(0.30t²)/dt = 2 * 0.30 * t = 0.60t.

Now substituting t = 50 s, we get:

ω = 0.60 * 50 = 30 rad/s.

The magnitude of the angular velocity of the centrifuge at t = 50 s is 30 rad/s.