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Calculate the distance the cylinder will pass until it starts rolling without sliding.

Thanks in advance!

- Thread starter giladbr
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- #1

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Calculate the distance the cylinder will pass until it starts rolling without sliding.

Thanks in advance!

- #2

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This gives you three scalar equations. If you put the coordinate frame so that y is normal to the ramp and x is down the ramp, then y_double_dot is zero and you only have to deal with x_double_dot, and w_dot.

Setting y_double_dot = 0 gives you the normal force and thus the friction force in terms of parameters you know (mass, theta, g, u). You know all the initial conditions, so you can integrate to find both x(t) and w(t).

If only we knew what t was, we would be done. You would plug t into x and solve. You still have one condition you haven't used yet. We want the time t when pure rolling occurs. What is the relation between w and x_dot for pure rolling? Plug in w and x_dot that you found into this condition and solve for t when rolling occurs.

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