A gyroscope slows from an initial rate of 32.0 rad/sec at rate of .700 rad/sec^2 . How many revolutions does it make before stopping?
To solve this problem, we need to find the time it takes for the gyroscope to stop. We can use the formula:
final angular velocity = initial angular velocity + (angular acceleration * time)
Since we want to find the time it takes for the gyroscope to stop, we set the final angular velocity to zero:
0 = 32 + (-0.700 * time)
Simplifying the equation, we get:
-32 = -0.700 * time
Dividing both sides by -0.700:
time = 32 / 0.700 ≈ 45.71 seconds
Now, we can find the number of revolutions by multiplying the time by the initial angular velocity:
number of revolutions = (initial angular velocity * time) / (2π)
number of revolutions = (32 * 45.71) / (2π)
number of revolutions ≈ 725.47
Therefore, the gyroscope makes approximately 725.47 revolutions before stopping.