A flywheel is rotating at speed of 1200 rpm its angular acclaration is 4 rad/s how many rotation it will be done before coming to rest
I assume you mean deceleration, or else it is speeding up.
Also, acceleration is measured in rad/s^2.
1200 rpm is 2400π/60 rad/s = 40 rad/s
so, if it loses 4 rad/s every second, how long will it take to lose all 40 rad/s?
Is 40 ans correct???????????
NO!
40rad/s
---------------- = 10s
4 rad/s^2
how could you possibly have come up with 40?
To find how many rotations the flywheel will make before coming to rest, we need to determine the deceleration of the flywheel. Deceleration is just negative acceleration, so in this case, it will be -4 rad/s^2.
The initial angular velocity of the flywheel is 1200 rpm, which can be converted to radians per second (rad/s) by multiplying by 2π/60:
Initial angular velocity = 1200 rpm * (2π/60) rad/s = 120π rad/s.
The final velocity of the flywheel when it comes to rest will be 0 rad/s because it has stopped rotating.
We can use the formula of motion for angular acceleration to find the time it will take for the flywheel to come to rest:
Final velocity = Initial velocity + (angular acceleration) * time.
Plugging in the values we know:
0 = 120π + (-4) * time.
Rearranging the equation:
4t = 120π.
Dividing both sides by 4:
t = 30π.
The time it takes for the flywheel to come to rest is 30π seconds.
To find the number of rotations, we can divide the time by the period of one rotation. The period of one rotation is the reciprocal of the frequency:
Period = 1 / frequency.
Frequency is the number of rotations per second, so:
Frequency = 1200 rpm / 60 = 20 Hz.
Period = 1 / 20 = 0.05 s.
Number of rotations = time / period = (30π) / 0.05 = 600π.
Therefore, the flywheel will make 600π rotations before coming to rest.