# Rotation of a wheel and axle

• schuksj
In summary, the conversation discusses a problem involving a rotationally symmetric axle wheel system joined to a fixed point O. The no-slipping condition leads to the equation d(phi)/dt=-(R/L)*S, which is derived using Euler's equation. The conversation also mentions the use of principal moments of inertia and the radius of the circle described by the wheel. The individual asking for help is struggling to find the correct answer and asks for a clue.
schuksj
I have a question about this problem. A rotationally symmetric axle wheel system is smoothly joined to a fixed point O.

l=distance from O to CM
m=mass of axle wheel system
Is and I are the principal moments of inertia relative to CM.
The axle is horizonal as the wheel rolls over the horizonal ground without slipping. The radius of the circle desrcibed by the wheel is L. Show that he no-slipping condition leads to:

d(phi)/dt=-(R/L)*S

I started with Euler's equation for the x component and set theta double dot to zero.

so d(phi)dt*sin(theta)*Is*S-(d(phi)/dt)^2*sin(theta)*cost(theta)=-mLsing(theta)

I said that I=mR^2/2 and Is-mR^2

plugging those into the equation I got:

d(phi)/dt*sin(theta)*mR^2*S-(d(phi)/dt)^2*cos(theta)*sin(theta)*mR^2/2=-mLsin(theta). I then took away the 2nd part of the equation because it is a higher order term and got that d(phi)/dt=-L/(R^2*S). This isn't exactly the right answer and I was wondering what I was doing wrong! Thanks.

I sitll have no idea how to do this problem. If someone could give me a clue I would really appreciate it. Thanks

## 1. How does the size of the wheel and axle affect rotation?

The size of the wheel and axle affects the rotation by changing the mechanical advantage. A larger wheel and smaller axle will have a greater mechanical advantage, making it easier to rotate, while a smaller wheel and larger axle will have a smaller mechanical advantage, making it more difficult to rotate.

## 2. What is the relationship between the force applied and the rotation of a wheel and axle?

The relationship between the force applied and the rotation of a wheel and axle is described by the principle of torque. The force applied to the wheel and axle creates a torque, which causes the wheel to rotate. The greater the force, the greater the torque, resulting in a faster rotation.

## 3. How does friction affect the rotation of a wheel and axle?

Friction can affect the rotation of a wheel and axle by creating resistance. The greater the friction, the more difficult it is to rotate the wheel and axle. This can be reduced by using lubrication or by using materials with lower coefficients of friction.

## 4. What is the purpose of having a wheel and axle system?

The purpose of a wheel and axle system is to provide a mechanical advantage, making it easier to move objects. It also allows for efficient transfer of rotational motion, making it useful for various applications such as transportation, machinery, and tools.

## 5. How does the direction of rotation affect the function of a wheel and axle system?

The direction of rotation does not affect the function of a wheel and axle system, as long as the force is applied in the same direction. The direction of rotation can be changed by reversing the direction of the force, or by using gears or pulleys to change the direction of the applied force.

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