- #1
PhysicsBoi1908
- 50
- 12
- Homework Statement
- A cylinder P of radius r[SUB]p[/SUB] is being rotated at a constant angular velocity ω[SUB]p[/SUB] with the help of a motor about its axis that is fixed. Another cylinder Q of radius r[SUB]q[/SUB] Free to rotate about its axis that is also fixed is touched with and pressed on P making angle θ between their axes. Soon after the cylinders are pressed against each other, a steady state is reached and cylinder Q acquires a constant angular velocity. Find the final angular velocity of Q and comment on frictional force.
- Relevant Equations
- v= ωr
A single pair of points will be in contact between P and Q. The frictional force will try to make the velocity of these points equal.
Say the final angular velocity of Q is ωq.
The velocity of points in contact can never be equal because of difference in directions of ωq and ωp. If I break ωqrq into horizontal and vertical components though, then I can write that its horizontal component must be equal to ωprp.
Thus
ωqrqcosθ=ωprp
And so we get ωq to be:
ωq=[tex]-ω_pr_p/r_qcosθ(sinθi+cosθj)
Which is wrong. The correct answer is:ωq=-ωprpcosθ/rq(sinθi+cosθj)
It seems that I was supposed to break ωprp into components instead. But I don't see why I should've done that.
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