2 dimensional motion problem

Question

(a) What are the period and speed of a person on a carousel if the person has an acceleration with a magnitude of 0.86 m/s2 when she is standing 3.6 m from the axis?

(b) What are her acceleration magnitude and speed if she then moves to a distance of 1.9 m from the carousel center and the carousel keeps rotating with the same period?

Answer 1

(a)

from  a = v²/r  we get  0.86 = v²/3.6

which leads to v = 1.76 m/s

period is the time it takes to complete a full cirle (your distance)

from v = d/t we get 1.76 = 2π(3.6) / T

which leads to T = 12.9s

 

 

(b)

again from v = d/t we get v = 2π(1.9)/12.9

which leads to v = 0.925 m/s

and from a = v²/r we get a = (.925)²/1.9

which leads to a = 0.45 m/s²

 

Answer 2

a)

a = v^2/r

8.6 = v^2/3.6

So, v = sqrt(.86*3.6) = 1.76 m/s

Period = 2pi r/v = 2pi*3.6/1.76 = 12.9 sec

b)

a = w^2 r = (2pi/T)^2 r = (2pi/12.9)^2 * 1.9 = .454 m/sec^2

v = w*r = (2pi/12.9) * 1.9 = .925 m/sec

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