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.
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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
 

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