A wheel of moment of inertia 0.136 kg · m2 is spinning with an angular speed of 5000 rad/s. A
torque is applied about an axis perpendicular to the spin axis. If the applied torque has a
magnitude of 67.8 N · m, the angular velocity of precession will be? Please help me solve this.
The answer is 100 rad/s.
To solve this problem, we can use the concept of torque and angular momentum.
First, let's define the terms and concepts involved:
- Moment of inertia (I): It represents the rotational inertia of an object and depends on its mass distribution.
- Angular speed (ω): It measures how fast an object is rotating.
- Torque (τ): It is the force applied perpendicularly to the radius of rotation, causing the object to rotate.
- Angular velocity of precession (ω_p): It represents how fast the spinning wheel as a whole will rotate due to the applied torque.
To find the angular velocity of precession (ω_p), we need to use the equation:
τ = I * ω * ω_p
Rearranging the equation, we can solve for ω_p:
ω_p = τ / (I * ω)
Plug in the given values:
ω_p = 67.8 N · m / (0.136 kg · m^2 * 5000 rad/s)
Perform the calculation:
ω_p = 0.099 rad/s
Therefore, the angular velocity of precession is approximately 0.099 rad/s, not 100 rad/s as mentioned in the answer.