A racing car completes 5 rounds of a circular track in 2 minutes. Find the radius of the track if the car has uniform centripetal
A racing car completes 5 rounds of a circular track in 2 minutes. Find the radius of the track if the car has uniform centripetal acceleration of π2/s2.
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Given: 5 rounds = 2πr(5),
t = 2minutes = 120s
To find: Radius (r)
Formula: acp = ω2r
Calculation: From formula,
acp = ω2r
∴ π2 = \(\frac{V^2}{r}\)
But v = \(\frac{2\pi r(5)}{t}=\frac{10\pi r}{t}\)
∴ π2 = \(\frac{100 \pi^2 r^2}{rt^2}\)
∴ r = \(\frac{120\times120}{100}\) =144m
The radius of the track is 144 m.
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