Question

The radius of a wheel of car is `0.4m`. The car is accelerated from rest by an angular acceleration of `1.5 rad//s^(2)` for `20 s`. How much distance will the wheel cover in this time and what will be its linear velaocity ?

Answer 1

Here, `r = 0.4m, omega_(1) = 0`,
`alpha = 1.5 rad//s^(2), t = 20 s, theta = ?`,
From `theta = omega_(1) + (1)/(2) alpha t^(2) = 0 + (1)/(2) xx 1.5 (20)^(2)`
`= 300 rad`.
Distance covered, `s = r theta = 0.4 xx 300 m`
`= 120 m`
Again, `omega_(2) = omega_(1) + alpha t = 0 + 1.5 xx 20`
`= 30 rad//s`
`upsilon = r omega_(2) = 0.4 xx 30 = 12 m//s`