The rotor of an electric motor uniformly accelerates to a speed of 1800 rpm from rest in 5 seconds and then the rotor decelerates uniformly to stop. If the total time elapsed from start to stop is 12.3 seconds, determine the number of revolutions made while acceleration and deceleration. What would be the reason for the longer time taken during stopping.
Answers
Explanation:
The rotor of an electric motor uniformly accelerates to a speed of 1800 rpm from rest in 5 seconds and then the rotor decelerates uniformly to stop. If the total time elapsed from start to stop i
Given:
i) The rotor of an electric motor uniformly accelerates to a speed of 1800 rpm from rest in 5 seconds and then the rotor decelerates uniformly to stop.
ii) The total time elapsed from start to stop is 12.3 seconds
To find:
The number of revolutions made while acceleration and deceleration.
Solution:
While acceleration,
initial speed (ωi) = 0
final speed (ωf) = 1800 rpm
= 1800/60 rps
= 30 rps
time(t) = 5 seconds
angular acceleration (α) = (ωf - ωi)/t
= (30 - 0)/5
= 6 rps²
θ = ωi x t + (1/2) x α x t²
= 0 + (1/2) x 6 x 5²
= 75 revolutions
While deacceleration,
initial speed (ωi) = 30 rps
final speed (ωf) = 0
time(t) = 12.3 - 5
= 7.3 seconds
angular acceleration (α) = (ωf - ωi)/t
= (0 - 30)/7.3
= -4.11 rps²
θ = ωi x t + (1/2) x α x t²
= 30 x 7.3 + (1/2) x (-4.11) x 7.3²
= 109.5 revolutions
The number of revolutions made while acceleration = 75, and
the number of revolutions made while deceleration = 109.5
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