## A modern F1 car can accelerate from 0 to 62 mile/h (100 km/h) in 2.05 s. What is the angular acceleration of its 170 mm radius wheels?

(F1 or formula 1 car is the common race car with big wheels and open cabin)

Explanation

The given data is for the linear motion of the car (wheel). However, we are asked to find quantity of angular motion. Therefore, (1) We convert the data of linear motion to the corresponding angular quantities. (2) After having the data in angular form, we apply the equations of angular motion to find the required quantities. We use the following formulae;

Linear velocity, v = ωr &Rightarrow; ω = v/r … (1)

ωf = ωi + αt … (2)
(α is the angular velocity).

Given
(1) Radius of the wheel = 170 mm = 0.170 m
(2) Initial velocity = vi = 0 m/s ⇒ Initial angular velocity = ωi = vi/r = 0 rad/s.
(3) Final velocity, vf = 62 mile/hr = 100 km/hr = (100 ×(1000)m/60 × 60s) = 27.8 m/s ⇒ ωf = 27.8/0.170 = 163.4 rad/s

(4) Time, t = 2.50 s

Required

Angular acceleration α of the wheel.

Solution

Put values in formula (2) from the given data,  