What's the relationship between T = r X F and T = I(alpha)?

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T = r X F defines torque, while T = I(alpha) represents Newton's second law for rotational motion. Both equations describe the same physical concept, linking torque to rotational dynamics. They can be equated to solve for specific variables in physics problems. Understanding this relationship clarifies their application in mechanics. The discussion emphasizes the simplicity of these foundational principles in physics.
mrbill
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What's the difference between T = r X F and T = I(alpha)? My book really sucks it up with the explanations. Both make sense to me. The answer is right in front of me I am sure, but I am just not catching it. One is merely an expression of Newton's second law? Bah, it can't be that simple!

MrBill.
 
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Originally posted by mrbill
Bah, it can't be that simple!
That's pretty much it. T = r X F is the definition of torque; T = I*α is Newton's 2nd law for rotational motion.
 
There is no difference, they're just 2 formulas relating to the same; that's why the two formulas can be set equal to each other in order to solve for a certain variable.
 
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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