Question

An electric fan has a constant angular velocity of 2.25 times 10^3 rpm. How many revolutions will it make in 11 s? rev Through how many radians will it rotate in 20 s? rad When the fan is turned off, it takes 6.9 s for it to stop. What is its angular acceleration (assumed constant) during this time? (Indicate the direction with the sign of your answer.) rad/s^2

Answer 1

angular velocity = 2.25 * 10^3 rpm

so,

fan makes 2.25 * 10^3 revolution in 1 min or 60 sec

revolution made by fan in 11 sec = 11 * 2.25 * 10^3 / 60

revolution made by fan in 11 sec = 412.5 rev

revolution made by fan in 20 sec = 20 * 2.25 * 10^3 / 60

revolution made by fan in 20 sec = 750 rev

1 rev has 2 * pi rad so

750 rev will have 750 * 2 * pi

revolution made by fan in 20 sec = 750 * 2 * pi

revolution made by fan in 20 sec = 4712.3889 rad

initial velocity = 2.25 * 10^3 rpm or 2.25 * 10^3 * 2 * pi / 60 rad/sec

final velocity = 0 rad/sec

by first equation of motion

v = u + at

0 = 2.25 * 10^3 * 2 * pi / 60 + a * 6.9

a = -34.1477 rad/sec^2

angular acceleration = -34.1477 rad/sec^2