Analytical question: circular rotation

AI Thread Summary
A point P on a smaller wheel cannot trace a straight line path inside a circular road due to the nature of circular motion. The discussion references an illustration from a physics resource to clarify the concept. Participants express confusion about the mechanics of circular rotation and how it relates to linear paths. The geometry involved complicates the idea of a straight line being traced. Understanding these principles is essential for grasping the relationship between circular motion and linear trajectories.
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Homework Statement
Circular Rotation
Relevant Equations
NO
Can a point P on the smaller wheel trace a straight line
path inside the circular road (like the walls of a well)
 
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Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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