Question

A car accelerates uniformly from rest and covers a distance of 76 m in 6.3 s. If the diameter of a tire is 43 cm, find the angular acceleration of the wheel. Answer in units of rad/s 2 .

Answer 1

43 cm.

Step-by-step explanation:

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Answer 2

17.81 rad/s²

Step-by-step explanation:

Distance = 76 m = s

Time taken = 6.3 s

Diameter of tire = 43 cm = 0.43 m

Radius of wheel = 43/2 = 21.5 cm = 0.215 m

Acceleration

`s=ut+(1)/(2)at^2\\\Rightarrow 76=0+(1)/(2)a6.3^2\\\Rightarrow a=76* 2(1)/(6.3^2)`

Angular acceleration

`\alpha=(a)/(R)\\\Rightarrow \alpha=(76* 2(1)/(6.3^2))/(0.215)\\\Rightarrow \alpha=17.81\ rad/s^2`

∴ Angular acceleration of the wheel is 17.81 rad/s²