Question
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?
Answers
GPT 3.5
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.
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.