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Hi,
I'm trying to model a wheel that is placed on top of a moving platform.
The problem is that I'm running into a situation that seems very counter intuitive. I'm not sure if its a problem with my model or not. I've attached a picture that demonstrates the problem.
To begin, neither the wheel nor the platform is moving. At some time (say t = 0), the platform begins accelerating in one direction (lets say its to the left) at a constant acceleration. For simplicity, I'm just assuming the mass of the platform is infinite (so that the wheel doesn't affect the motion of the platform).
So the wheel starts to accelerate with the platform, but also rolls in a direction that opposes the movement of the platform (assume it never slips). I've attached my derivation of the force and torque acting on the wheel as the platform moves.
Now the problem comes in when I look at how many rotations the wheel makes. If the radius of the wheel is R and the length of the platform is 2πR (the circumference of the wheel), then I would expect the wheel to make exactly one full rotation before falling off the platform. Instead I find that it depends on the moment of inertia of the wheel, for example, a disk makes 2 rotations.
Can someone explain if this is true, or just a problem with my derivation?
I'm trying to model a wheel that is placed on top of a moving platform.
The problem is that I'm running into a situation that seems very counter intuitive. I'm not sure if its a problem with my model or not. I've attached a picture that demonstrates the problem.
To begin, neither the wheel nor the platform is moving. At some time (say t = 0), the platform begins accelerating in one direction (lets say its to the left) at a constant acceleration. For simplicity, I'm just assuming the mass of the platform is infinite (so that the wheel doesn't affect the motion of the platform).
So the wheel starts to accelerate with the platform, but also rolls in a direction that opposes the movement of the platform (assume it never slips). I've attached my derivation of the force and torque acting on the wheel as the platform moves.
Now the problem comes in when I look at how many rotations the wheel makes. If the radius of the wheel is R and the length of the platform is 2πR (the circumference of the wheel), then I would expect the wheel to make exactly one full rotation before falling off the platform. Instead I find that it depends on the moment of inertia of the wheel, for example, a disk makes 2 rotations.
Can someone explain if this is true, or just a problem with my derivation?