An astronaut is being tested in a centrifuge. the centrifuge has a radius of 10.4 m and in starting, rotates according to ϕ = (0.326 rad/s2)t2. when t = 5.60 s, what are the astronaut's
(a) angular speed,
(b) tangential speed,
(c) tangential acceleration
(d) radial acceleration?

3.6512 rad/s

37.97248 m/s

6.7808 m/s²

138.645118976 m/s²

Explanation:

r = Radius of centrifuge = 10.4 m

Differentiating with respect to time

At t = 5.6 s

Angular speed is 3.6512 rad/s

Tangential speed is given by

The tangential speed is 37.97248 m/s

Angular acceleration is given by

Tangential acceleration is given by

The tangential acceleration is 6.7808 m/s²

Radial acceleration is given by

The radial acceleration is 138.645118976 m/s²

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.