The blades of a motor rotate at a rate of 4401 rpm. When the motor is turned off, the blades slow to a new angular speed of 430 rpm in 4.93 seconds. What is the angular acceleration of the blades (in rads/sec^2)?
Vo=4401rev/min * 6.28rad/rev * 1min/60s=
460.6 m/s
V = 430 * 6.28/60 = 45 m/s.
a=(V-Vo)/t = (45-460.6)/4.93=-84.3 m/s^2
Correction:
Vo = 460.6 rad/s
V = 45 rad/s
a = -84.3 rad/s^2
To find the angular acceleration of the blades, we need to use the formula:
angular acceleration (α) = (final angular velocity - initial angular velocity) / time
First, let's convert the initial angular velocity in rpm (revolutions per minute) to radians per second:
initial angular velocity = 4401 rpm
1 revolution = 2π radians
So, initial angular velocity = (4401 rpm) * (2π radians/1 minute) * (1 minute/60 seconds) = 461.35 radians/second
Next, let's convert the final angular velocity in rpm to radians per second:
final angular velocity = 430 rpm
final angular velocity = (430 rpm) * (2π radians/1 minute) * (1 minute/60 seconds) = 45.15 radians/second
Now, we can calculate the angular acceleration:
angular acceleration = (final angular velocity - initial angular velocity) / time
angular acceleration = (45.15 - 461.35) / 4.93 seconds = -83.353 rads/sec^2
Therefore, the angular acceleration of the blades is approximately -83.353 rads/sec^2.