Direction of forces (centripetal/friction/tension)

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Centripetal acceleration always points towards the center of the circular path, while tension in a string also directs inward when an object is spun. In contrast, friction acts opposite to the direction of motion, which means it points outward when a car drives in a circle. Understanding these force directions is crucial for analyzing motion in circular dynamics. The relationship between these forces helps clarify their roles in maintaining circular motion. Accurate identification of force directions is essential for solving physics problems related to circular motion.
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my general question is how do you know what direction these forces point in, particularly when spinning an object on a string (either horizontally or vertically) or when say a car is driving in a circle.

the first one has centripetal acceleration and tension. the 2nd example has centripetal acceleration and friction.

how do you know what direction they point in? my guess is centripetal points in and the other two (friction/tension) point out but I am not sure. can someone please help? thanks.
 
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Thread 'Variable mass system : water sprayed into a moving container'

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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