Apparent Initial Acceleration due to Precession of Wheel Gyroscope?

In summary, the center of mass of a system acts as a point where all the mass is concentrated and forces can act on it. In the example of a wheel gyroscope, the center of mass is in the middle of the wheel and when the wheel is spun and let go, it undergoes precession due to torque by gravity changing its angular momentum. The circular motion of the center of mass is caused by the support, and if the support is not grounded, the center of mass will rotate around it. However, in the case of a heavy top, pseudoregular precession may occur due to a torque from gravity and a reaction force from the chain.
  • #1
HakimTem
3
0
The center of mass of a system is defined as a point that acts as if all the mass is concentrated on that one point whereby all forces may act on it. With a wheel gyroscope as an example where the center of mass is in the middle of the wheel when the wheel is spun and let go, the wheel undergoes precession whereby it rotates around its support. This comes from the nature of torque by gravity on the wheel changing its angular momentum. However, why does the center of mass gain an acceleration when it's let go to pursue a circular orbit? And which force causes such acceleration?
 
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  • #2
The force for the circular motion of the CoM comes from the support. If you spin the gyroscope on something slippery the CoM will stay in place and the support will make a circle instead.
 
  • #3
So if using this as a diagram
f0409.gif

how does the wheel initially start moving in the horizontal plane and where are the forces labeled on the diagram?
 
  • #4
That diagram is not accurate. The chain will not hang vertically, but will make a small angle with the vertical. This small angle with the vertical will produce a restoring force like any pendulum. The restoring force will serve as the centripetal force for the circular motion of the CoM as it precesses.
 
  • #5
So if the support is not supported by the ground and is allowed to move with the wheel then it would rotate around the center of mass?
 
  • #7
HakimTem said:
So if the support is not supported by the ground and is allowed to move with the wheel then it would rotate around the center of mass?
Yes. If the support cannot provide any horizontal force, but only a vertical force, then the center of mass will not move. It will just precess around the center.
 

1. What is the apparent initial acceleration due to precession of a wheel gyroscope?

The apparent initial acceleration due to precession of a wheel gyroscope is the perceived acceleration of the gyroscope when it is first set in motion. This is caused by the torque applied to the gyroscope as it begins to precess, which creates a force that is felt as an acceleration.

2. How is the apparent initial acceleration calculated?

The apparent initial acceleration can be calculated using the formula a = ω x v, where a is the acceleration, ω is the angular velocity, and v is the linear velocity of the gyroscope.

3. What factors affect the apparent initial acceleration?

The apparent initial acceleration is affected by the mass and shape of the gyroscope, the speed at which it is spun, and the angle at which it is tilted. Other factors such as air resistance and friction can also play a role.

4. How does the apparent initial acceleration impact the motion of the gyroscope?

The apparent initial acceleration causes the gyroscope to precess, or rotate, in a direction perpendicular to the applied torque. This motion can affect the stability and orientation of the gyroscope as it continues to spin.

5. What practical applications does understanding the apparent initial acceleration have?

Understanding the apparent initial acceleration is important in fields such as aviation and navigation, where gyroscopes are used for stability and orientation. It can also have applications in robotics and other mechanical systems that use gyroscopic motion.

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