a) A car travels around a traffic circle (a.k.a. round-about, roundie, rotary) a

Question

a) A car travels around a traffic circle (a.k.a. round-about, roundie, rotary) at a constant speed of 180 km/hr. If the path of travel is cicular with a diameter of 680 m, determine the acceleration of the auto in g's.

b) The same car travels around the same traffic circle at the same constant speed of 180 km/hr. If the path of travel is again cicular with a diameter of 680 m, determine the angular velocity of the auto in rev/min (rpm).

c) Have you seen 2001 A Space Odyssey? The 1968 movie opens with a spectacular scene of a rocketship docking with an orbiting spacestation. Google: 2001 a space odyssey docking scene and note the space station with its circular rim that forms the space station's main corridor or passagewar. Now, let's assume that the diameter of the space station is 900 m and determine the angular velocity in rev/hr necessary to 'create' an artificial gravity of 6/10 g.

Explanation / Answer

a)

r=d/2=680/2 = 340m

v=180km/hr = (180000m/3600s) = 50m/s

a= v2/r = 50^2/340 = 7.35m/s2

g=9.81m/s2

a/g = 7.35/9.81 = 0.75

a= 0.75g

b)

=v/r = 50/340 = 0.147 rad/s =

1rev=2 rad = > 1rad = 1rev/2

1min= 60s => 1s= 1min/60

= 0.147 rad/s = [(0.147 rad/s)*(1rev/2)]/(1min/60)

= 1.4 rev/min

c)

a=(6/10)g = 0.6g = 0.6*9.81m/s2 = 5.886 m/s2

r=d/2=900/2= 450m

a= 2r

2 = a/r

= sqrt(a/r)

= sqrt(5.886/450)

= 0.1144 rad/s

1rev=2 rad = > 1rad = 1rev/2

1hr = 3600s => 1s= 1hr/3600

= 0.1144rad/s = [(0.1144 rad/s)*(1rev/2)]/(1hr/3600)

= 65.55rev/hr

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