A modern F1 car can accelerate from 0 to 62 mile/h (100km/h) in 2.50 s, What is the angular acceleration of its 170 mm-radius wheels? (65.17 rad s⁻²) 


Given:

Initial velocity of the car = vi = 0 km/h = o m/s
Final velocity of the car = vi = 100 km/h = `\frac {100 ｘ 1000}{60 ｘ 60 }` m/s = 28 m/s
Time interval = Δt = 2.50 s
Radius of the wheel = r = 170 ｘ10³ m = 0.170 m

To Find:

Angular acceleration = 𝛂 = ?

Solution:

The formula for angular acceleration is

a  = r 𝛂

or

𝛂  = `\frac {a}{r }` --------------(1)

But a = `\frac {Δv}{Δt }` where  Δv = vf - vi so, 

a = `\frac {vf - vi}{Δt }`

by putting the values in equation (1) 

𝛂  = `\frac {vf - vi}{r Δt}`

by putting values

𝛂  = `\frac {28 ms⁻¹ - 0 m s⁻¹}{0.170 m ｘ 2.50 s}`

𝛂  = `\frac {28 m s⁻¹}{0.425 ms}`

𝛂  = 65.9 rad s⁻²----------------------Ans.



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