Question

Pilots can be tested for the stresses of flying high-speed jets in a whirling "human centrifuge," which takes 1.3 min to turn through 22 complete revolutions before reaching its final speed.
a)What was its angular acceleration (assumed constant)?
Express your answer using two significant figures.
b)What was its final angular speed in rpm ?
Express your answer using two significant figures

Answer 1

(a) The angular acceleration will be 26.035 rev/$min^{2}$.

(b) The final angular velocity is expected to be 33.846 rev/min.

Given.

t=1.3 min, Θ=22 rev, $ω_{i}$=0

We know, Θ= $ω_{i}$t+$\frac{1}{2}$$\alpha$$t^{2}$

22=0+$\frac{1}{2}$$\alpha$$1.3^{2}$

$\alpha$=26.035 rev/$min^{2}$

$ω_{f} =ω_{i}+\alpha t$=0+26.035*1.3=33.846 rev/min

Angular velocity

An object's rate of change in angular position or orientation over time is depicted by its angular velocity, rotational velocity, or both ( or ), also known as the angular frequency vector (i.e. how quickly an object rotates or revolves relative to a point or axis). The direction of the pseudovector is normal to the instantaneous plane of rotation or angular displacement, and its magnitude denotes the angular speed, or the rate at which the item rotates or revolves. It is customary to use the right-hand rule to specify the direction of angular motion. A general definition of angular velocity is "angle per unit time" (angle replacing distance from linear velocity with time in common). Radians per second is how angles are measured in the SI.

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