A DVD is spinning at 180 rpm’s. Calculate its angular acceleration when it increases to 240 rpms’s in 2 seconds. (Remember, convert rpm’s to radians/second)
Vo = 180rev/min * 6.28rad/rev * (1/60)min/s = 18.84rad/s.
Vf = 240/180 * 18.84 = 25.12rad/s.
a = (Vf-Vo)/t = 25.12 - 18.84) / 2 = 3.14rad/s^2.
To calculate the angular acceleration of the spinning DVD, we first need to convert the angular velocity from RPM (revolutions per minute) to radians per second.
1 revolution = 2π radians
So, to convert RPM to radians per second, we multiply by 2π/60 (since there are 60 seconds in a minute):
180 RPM * (2π/60) = 6π radians/second
Now, we need to find the change in angular velocity. From 180 RPM to 240 RPM, the change is:
240 RPM - 180 RPM = 60 RPM
Converting this to radians per second:
60 RPM * (2π/60) = 2π radians/second
Finally, we can calculate the angular acceleration using the formula:
angular acceleration = change in angular velocity / time
angular acceleration = (2π radians/second) / (2 seconds) = π radians/second²
Therefore, the angular acceleration of the DVD is π radians/second².