A flywheel turns through 40 rev as it slows from an angular speed of 1.5 rad/s to a stop. (a) Assuming a constant angular acceleration, find the time for it to come to rest. (b) What is its angular acceleration

The time of motion is 333.3 s

The angular acceleration is -0.0045 rad/s²

Explanation:

Given;

angular distance of the flywheel, θ = 40 rev

initial angular speed, = 1.5 rad/s

When the wheel comes to rest, the final angular speed, = 0

The angular acceleration is calculated as follows;

The time of motion is calculated as;

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west