The propeller of a plane rotate clockwise at 26900 rpm. What is the angular acceleration (in rad/s2) of the propeller if it takes 8.00 s to come to a standstill?
(-26900/60*2pi rad/s)/(8.00s) = -352.12 rad/s^2
To find the angular acceleration of the propeller, we need to use the formula:
angular acceleration = change in angular velocity / time
First, we need to convert the given rotation speed from rpm to radians per second (rad/s). Since 1 rpm is equal to (2π/60) rad/s, we can find the angular velocity (ω) of the propeller using the formula:
angular velocity = rotation speed in rpm * (2π/60)
Substituting the given rotation speed of 26900 rpm:
ω = 26900 rpm * (2π/60)
Now, we can find the change in angular velocity using the formula:
change in angular velocity = final angular velocity - initial angular velocity
Since the propeller comes to a standstill, the final angular velocity is 0 rad/s. The initial angular velocity can be calculated using the formula:
initial angular velocity = 26900 rpm * (2π/60)
Finally, we can calculate the angular acceleration by dividing the change in angular velocity by the time taken, as given:
angular acceleration = change in angular velocity / time
Substituting the values, the formula becomes:
angular acceleration = (0 rad/s - (26900 rpm * (2π/60))) / 8.00 s
Now, we can calculate the angular acceleration.