A 25-kg girl on the outside of a merry-go-round (with a diameter of 2.6 m) exper

Question

A 25-kg girl on the outside of a merry-go-round (with a diameter of 2.6 m) experiences a constant angular acceleration of 0.49 rad/s2 (thanks to her friend pushing her). She starts from rest, and at some later time she has a linear (tangential) speed of 3.1 m/s. Determine a) The time, t, it took her to reach the linear speed of 3.1 m/s. b) How far, in radians, she traveled while accelerating to 3.1 m/s. c) How far, in meters, she traveled while accelerating to 3.1 m/s. d) Her tangential acceleration while being pushed.

Explanation / Answer

given

m = 25 kg

d = 2.6 m

r = d/2 = 2.6/2 = 1.3 m

alfa = 0.49 rad/s^2

vf = 3.1 m/s

vi = 0

so, wi = 0

wf = vf/r = 3.1/1.3 = 2.38 rad/s

a) use, alfa = (wf - wi)/t

==> t = (wf - wi)/alfa

= (2.38 - 0)/0.49

= 4.86 s

b) use, wf^2 - wi^2 = 2*alfa*theta

==> theta = (wf^2 - wi^2)/(2*alfa)

= (2.38^2 - 0^2)/(2*0.49)

= 5.78 rad

c) use, s = r*theta

= 1.3*5.78

= 7.51 m

d) a_tan = r*alfa

= 1.3*0.49

= 0.64 m/s^2

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