Reasoning behind predicting a gyroscope's motion

[Fibo112]

Hello. I am reading about the gyroscope and it says that it's motion, initially, is to rotate around the center. I understand why this makes sense since the initial angular momentum is pointing towards the center and the torque is towards the right the rotation changes the angular momentum according to the torque, we can even calculate the speed of the rotation. So now the question...Do we predict this motion solely by saying "this is the only motion that allows the angular momentum to change as it should according to the torques, so the normal force must cancel the gravitation"?

 

[Mgcini Keith Phuthi]

I am a bit confused by which rotations you refer to at what point but I'll assume you have a 'spinning' gyroscope (along the gyroscope's axis) whose axis is 'precessing' (about where the gyroscope is pivoted) under the influence of gravity. The motions can be found by carefully considering the direction of the torque and aligning the change in angular momentum in the same direction i.e. given a spin direction, the direction of precession is given so that the effect of a positive torque increases angular momentum in that direction. And yes, the weight must cancel out the normal contact force since there is equilibrium in that direction.

 

[Fibo112]

I am a bit confused by which rotations you refer to at what point but I'll assume you have a 'spinning' gyroscope (along the gyroscope's axis) whose axis is 'precessing' (about where the gyroscope is pivoted) under the influence of gravity. The motions can be found by carefully considering the direction of the torque and aligning the change in angular momentum in the same direction i.e. given a spin direction, the direction of precession is given so that the effect of a positive torque increases angular momentum in that direction. And yes, the weight must cancel out the normal contact force since there is equilibrium in that direction.

Thanks for the reply. How exactly do we know that there is equillibrium in the vertical direction?

 

[sophiecentaur]

Thanks for the reply. How exactly do we know that there is equillibrium in the vertical direction?

Because it's centre of mass is not rising or falling. It is just precessing, hanging at the same angle.

 

[Fibo112]

But how do we know that the center of mass isn't rising or falling?

 

[DaTario]

In fact, a more basic description of the gyroscope precession can be given in terms of the unbalance of centripetal forces. I guess this approach is more appropriate for the study you want to do.
reference: Ernest F. Barker, "Elementary Analysis of the Gyroscope", Am. J. of Phys. 28, 808 (1960)
http://dx.doi.org/10.1119/1.1936009

 

[Fibo112]

I am not able to access the link...I think my confusion might be coming from the fact that I don't yet understand the general reasoning processes in physics. My way of explaining that the normal force is equal to the weight would be: if the normal force is not equal to the weight the body will move verticaly causing a change in angular momentum in a direction in which there is no torque => contradiction. Is this reasoning correct? How would you guys have reasoned?

 

[Mgcini Keith Phuthi]

I am not able to access the link...I think my confusion might be coming from the fact that I don't yet understand the general reasoning processes in physics. My way of explaining that the normal force is equal to the weight would be: if the normal force is not equal to the weight the body will move verticaly causing a change in angular momentum in a direction in which there is no torque => contradiction. Is this reasoning correct? How would you guys have reasoned?

A net force would cause a body to linearly accelerate in the direction of the force. In this case there is zero net force so the gyroscope does not linearly accelerate. However, because the weight and normal force are not aligned, there is a net torque, this is what is responsible for the precession.

 

[Fibo112]

A net force would cause a body to linearly accelerate in the direction of the force. In this case there is zero net force so the gyroscope does not linearly accelerate. However, because the weight and normal force are not aligned, there is a net torque, this is what is responsible for the precession.

I understand this, but I don't see how it answers my question...I must be missing something

 

[FactChecker]

Trying to tilt the axis of rotation and associated rotational momentum vector in one direction means that there is a component added to the rotation vector. That component represents a circular acceleration in a different direction. As long as the secondary rotational acceleration is unopposed, there is a third rotational force that will stop the initial tilt. That opposes the gravitational force and the net motion is the circular procession. That is, all the initial force to tilt the gyroscope is converted into circular acceleration of the procession -- there is no force left to tilt the gyro more.