Calculate the linear acceleration of a particle moving in a circle of radius ` 0.5m` at the iunstant when its angular velcity is ` 2 rad s^(-1)` and its angular acceleaation is 1 6 rad s^(-2)`.

Explanation

Here, ` r=0.5 , omega=2 rad//s , alpha =6 rad s^(-20`
Tangential acceleration, ` a_T= ralpha =0.5 xx 6`
`= 2.0 ms^(-2)`
Cetripetal acceleration, ` a_C = r omega^2 =0.5 xx2^2`
`= 2.0 ms^(-2)`
Total linera acceleration , ` a= sqrt(a_T^2 +a_C^2)`
:. ` a = sqrt ((3.0)^2 + (2.0)^2 ) =3.6 ms^(-2)`
If ` vec a` makes an angle ` theta` `vec a_T`, then
` tan theta = a_C/a_T = 2/3 = 0 6667 = tan 33^@ 42' `
` theta =33^2 42' with `a_T`.