Question

A flywheel with a diameter of 1.20 m is rotating at an angular speed of 200 rev/min. (a) What is the angular speed of the flywheel in radians per second? (b) What is the linear speed of a point on the rim of the flywheel? (c) What constant angular acceleration (in revolutions per minute-squared) will increase the wheel’s angular speed to 1000 rev/min in 60.0 s? (d) How many revolutions does the wheel make during that 60.0 s?

Answer 1

(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,

$w = 200 X \frac{2\pi }{60} \\\\w = 200 X \frac{2 X 3.14}{60} \\\\w = 20.944 rad/sec$

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

                      $v = 20.944 X \frac{1.2}{2}\\\\v = 12.6m/s$

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)

$1000 = 200 + a \frac{60}{60}$

$a = \frac{1000 - 200}{1} \\\\a = 800 rev/min^2$

Thus, constant angular acceleration, a = 800rev/min²

(d) The number of revolutions that a flywheel makes in 60 seconds

$n = wt + \frac{1}{2}at^2\\ \\n = 200 X \frac{60}{60} + \frac{1}{2} X 800 X (\frac{60}{60})^2\\ \\n = 600 rev$

Thus, the number of revolutions that a flywheel makes in 60 seconds is 600 revolutions.