Answer:
α = 3.59 [rad/s^2]]
Explanation:
First we have to convert the values of the angular speeds of revolutions per minute to radians on second.
wf = final angular velocity = 460 [rpm]
wo= initial velocity = 48 [rpm]
t = time = 12 [s]
[tex]460 [\frac{rev}{min}]* [\frac{2\pi rad}{1 rev} ]*[\frac{1min}{60seg} ] = 48.17[\frac{rad}{s} ]\\48 [\frac{rev}{min}]* [\frac{2\pi rad}{1 rev} ]*[\frac{1min}{60seg} ] = 5.02[\frac{rad}{s} ][/tex]
now we can replace, in the following equation:
[tex]w_{o}=w_{i} +\alpha *t\\where:\\\alpha = angular acceleration [rad/s^{2}]\\replacing:\\\alpha =\frac{w_{o} -w_{i} }{t} \\\alpha alpha =\frac{48.17-5.02 }{12} \\\alpha =3.59[\frac{rad}{s^{2} } ][/tex]
