Respuesta :
(a) Angular speed, ω = 20.944rad/sec
(b) Linear speed, v = 12.6m/s
(c) Constant angular acceleration, a = 800rev/min²
(d) The number of revolutions that a flywheel makes in 60 seconds is 600 revolutions.
Explanation:
Given-
Diameter of the flywheel, D = 1.2m
Angular speed of the flywheel, ω = 200 rev/min
(a) Angular speed of the flywheel in rad/sec
To convert angular speed from rev/min to rad/sec, we multiply the number with 2π/60
Thus,
[tex]w = 200 X \frac{2\pi }{60} \\\\w = 200 X \frac{2 X 3.14}{60} \\\\w = 20.944 rad/sec[/tex]
Thus, angular speed, ω = 20.944rad/sec
(b) Linear speed of a point on the rim of the flywheel = ?
We know,
linear speed, v = ω X r (r is the radius)
v = ω X D/2
[tex]v = 20.944 X \frac{1.2}{2}\\\\v = 12.6m/s[/tex]
Thus, Linear speed, v = 12.6m/s
(c) Constant angular acceleration = ?
The angular velocity of the flywheel is increased from ω = 200 rev/min to ω2 = 1000 rev/min in 60 seconds.
Thus, the constant angular acceleration can be calculated as
ω2 = ω + at ( t is the time at which the angular speed can be
increased)
[tex]1000 = 200 + a \frac{60}{60}[/tex]
[tex]a = \frac{1000 - 200}{1} \\\\a = 800 rev/min^2[/tex]
Thus, constant angular acceleration, a = 800rev/min²
(d) The number of revolutions that a flywheel makes in 60 seconds
[tex]n = wt + \frac{1}{2}at^2\\ \\n = 200 X \frac{60}{60} + \frac{1}{2} X 800 X (\frac{60}{60})^2\\ \\n = 600 rev[/tex]
Thus, the number of revolutions that a flywheel makes in 60 seconds is 600 revolutions.
