Uniform circular motion of a particle

AI Thread Summary
A particle moves in uniform circular motion with a radius of 1.5 meters, completing 4 revolutions in 6 seconds, resulting in a speed of approximately 6.28 m/s. The radial acceleration is calculated as 26.29 m/s² using the formula ar = -v²/r. The direction of the radial acceleration points towards the center of the circular path. The tangential acceleration is determined to be zero, indicating that the particle maintains a constant speed without any tangential acceleration. The discussion emphasizes understanding the relationships between speed, radial acceleration, and tangential acceleration in circular motion.
southernbelle
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Homework Statement


A particle is moving at a constant speed around a circle of radius 1.5 meters, and it completes 4 revolutions in 6 seconds.
a) What is its speed?
b) What is its radial acceleration?
c) In which direction does ar point?
d) What is it tangential acceleration, at?


Homework Equations


ac=v2/r
T=2pie times r/v
at= derivative of v/t
ar = -v2/r
ac = ar + at


The Attempt at a Solution


a.
6=8(pie)(1.5)/v
answer: 2pie
v=6.28 m/s

b.
ar = -v2/r
ar = 39.43/1.5
ar = 26.29 m/s2

c. I am not sure how to get the direction.

d. ac= ar + at
26.29 = 26.29 + at
at = 0?
 
Physics news on Phys.org
think about what would happen if it accelerated constantly tangentially, and describe that motion, and see if it fits with your problem
 
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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