Gyroscope/bicycle wheel question

Hi there...

As English is not my native language I want to apologise up front for any mistakes.

I have tried asking my question in a local Dutch forum, but I have not received a satisfactory answer yet. So, I thought I will try internationally.

Imagine a fast spinning wheel, like in a gyroscope. Let's assume there's no friction of any kind, so if you let it it will keep spinning at the same speed.

Now you tilt the spinning wheel by 90 degrees. Of course it resists this movement (I think conservation of angular momentum is the right word?), but you don't allow it to move in any other way than the 90 degrees tilt that you intend.

To move the wheel this way you put in energy. You have to overcome the resistance all the way.

My question is: Where does this energy go?

I don't mean any heat resulting from friction. You put in energy, you add energy to the spinning-wheel-system, where does it go?

Does the speed (rate?) of spinning change? Decelerate? Accelerate?

I hope my question is clear, and I'm looking forward to any replies. Thank you.

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AlephZero
Homework Helper
You don't put in any energy. The movement is at right angles to the direction of the force, so scalar product of force . distance = 0.

If a truck is moving along a horizontal road, the weight of the truck doesn't do any work as the truck moves, for the same reason.

I'm having trouble posting a reply... I'll try again, hope I don't post double...

AlephZero
Homework Helper
Eurpoeman, I've been designing and analysing rotating machinery for more than 30 years. I know what a gyroscope is and how it works.

Suppose your bike wheel is vertical, and you want to turn it so it is horizontal. You move one end of the axle up and the other end down. The forces you apply to stop the gyroscope effect are forwards and backwards, at right angles to the direction you move. The work done by the scalar product of the force and displacement vectors is zero.

Aleph, I never meant to question your knowledge, I just thought I failed to make my question clear to you. Thank you for your new reply.

I'm afraid I still don't understand though. What you say would mean that any two-handed action, rotating something with hands on opposite sides, would mean zero work. Like turning the helm wheel of a ship... An old ship, not "fly by wire" :)

AlephZero
Homework Helper
No, if you turn the helm of a ship you apply a force tangential to the wheel. You move in the same direction as the force, not at right angles to it.

If the bike wheel is not rotating and you apply a force up on one side and down on the other, then you are doing work. You give the wheel some kinetic energy while it is turning.
To stop the axle changing direction, you have to apply a force in the opposite direction. After it has stopped, the total amount of work you did was zero. The work to start the wheel moving = - the amount of the work to stop it again. Once the axle is turning, if you apply no force it will keep turning at the same speed (Newton's Laws).

But if the wheel is rotating like a gyroscope and you apply a force up on one side of the axle and down on the other side, the axle will turn in the horizontal plane, not in the vertical plane. If you stop applying a force, the axle will immediately stop changing direction. You don't have to apply a force in the opposite direction to stop it.

For a non-rotating wheel, the angular acceleration of the axle is proportional to the torque you apply. For a rotating wheel (a gyroscope), the angular velocity of the axle is proportional to the torque. That's an important difference for understanding how gyroscopes behave.

mgb_phys
Homework Helper
When you ignore things like friction in a physics question you often get a different behaviour to what you feel in the 'real' world.
In physics you do no work by pushing a truck along a level surface, but you definately feel something in your muscles.

Gyroscopes are complicated because of this. Many people spend their lives designing them - like AlephZero, but many more people spend their lives designing impossible machines because they misunderstood how they work.

Hi there...

As English is not my native language I want to apologise up front for any mistakes.

I have tried asking my question in a local Dutch forum, but I have not received a satisfactory answer yet. So, I thought I will try internationally.

Imagine a fast spinning wheel, like in a gyroscope. Let's assume there's no friction of any kind, so if you let it it will keep spinning at the same speed.

Now you tilt the spinning wheel by 90 degrees. Of course it resists this movement (I think conservation of angular momentum is the right word?), but you don't allow it to move in any other way than the 90 degrees tilt that you intend.

To move the wheel this way you put in energy. You have to overcome the resistance all the way.

My question is: Where does this energy go?

I don't mean any heat resulting from friction. You put in energy, you add energy to the spinning-wheel-system, where does it go?

Does the speed (rate?) of spinning change? Decelerate? Accelerate?

I hope my question is clear, and I'm looking forward to any replies. Thank you.
I think that's the problem---if you 'turn' the wheel (work), there will be friction at the axil/bearing, and that's where the 'energy' is lost.

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