Respuesta :
To reach the final angular speed of 7200rpm, a computer hard disks that starts from rest then speeds up with an angular acceleration of 190 rad/s^2 will need 238 revolutions.
What is angular speed?
It is the speed of the object in rotational motion. Distance travelled is represented as Φ and is measured in radians. The time taken is measured in terms of seconds. Therefore, the angular speed is articulated in radians per seconds. To reach a certain angular speed, the object needs to accelerate which named as angular acceleration.
How to calculate the revolution of the disk has to make?
From the question given
initial angular speed ωi = 0 rad / s (from rest)
final angular speed ωf = 7,200rpm = 7,200 * (2*π/60) = 753.98 rad / s
Angular acceleration α = 190 rad / s^2
Let's find the value of θ as the angular displacement
Now, let's use the third equation of rotational motion
ωf^2 - ωi^2 = 2 * α * θ
753.98^2 - 0^2 = 2 * 190 * θ
568,485.8404 = 380θ
θ = 1,496.015 rad
θ = 1,496.015 / 2*π
θ = 238.22 rev (rounded)
Because angular acceleration is constant, then we can use constant angular acceleration equation.
Therefore, the disk has made 238 revolutions in the time that it was accelerating.
Learn more about angular speed https://brainly.com/question/15016937
#SPJ4
