a turn table is turing at a rate of 45 rad/sec and comes to rest after 5 second.how many rotation does it make before coming to rest?

average angular velocity during stop = 45/2 = 22.5 rad/sec

so
total angle = 22.5 rad/s * 5 s = 112.5 radians

112.5 radians / 2 pi radians/revolution
= 17.9 revolutions

To find the number of rotations the turntable makes before coming to rest, we need to determine the total angle it covers during the 5-second period.

The formula to find the angle covered by an object rotating at a certain rate is given by:

θ (angle) = ω (angular velocity) × t (time)

Here, the angular velocity (ω) is given as 45 rad/sec and the time (t) is given as 5 seconds.

θ = 45 rad/sec × 5 sec
θ = 225 radians

Since there are 2π radians in one complete revolution, we can convert the total angle (225 rad) to the number of rotations:

Number of rotations = θ / (2π)

Substituting the value of θ:

Number of rotations = 225 rad / (2π)
Number of rotations ≈ 35.9 rotations (rounded to one decimal place)

Therefore, the turntable makes approximately 35.9 rotations before coming to rest.