Quick units question on uniform circular acc

AI Thread Summary
In uniform circular motion, the centripetal acceleration is crucial for maintaining the circular path. The discussion centers on calculating the dot product of acceleration (a) and velocity (v), as well as the cross product of radius (r) and acceleration (a). Both calculations yield a result of zero, indicating orthogonality. The user seeks clarification on the units involved in these operations, specifically through dimensional analysis. Understanding the dimensions of velocity and acceleration is essential for confirming the results.
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Homework Statement



A centripetal-acceleration addict rides in uniform circular motion with period T = 2.3 s and radius r = 2.80 m. At t1 his acceleration is = (6.60 m/s2) + (-2.40 m/s2). At that instant, what are the values of (a)v dot a and (b) r X a ?

Homework Equations



i know the answers, I am just really unsure of the units

The Attempt at a Solution



the answers are both zero but what are the units?
 
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Can you do dimensional analysis? For example v dot a has dimensions of velocity times dimensions of acceleration.
 
yeah, i got it, i just wasn't sure if that was quite the right approach
thanks though
 
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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