A wheel rotates around a stationary axis so that the rotation angle `theta` varies with time as `theta=2t^(2)` radian. Find the total acceleration of the point `A` at the rim at the moment `t=0.5 s` If the radius of wheel is `1 m`.

Explanation

`theta=2t^(2) radian`
`omega=(d theta)/(dt)=4t`
`alpha=(domega)/(dt)=4`
At `t=0.5 s`,
`omega=4t=4xx0.5=2 rad//s`
`a_(c)=omega^(2)R=(2)^(2)xx1=4 m//s^(2)`
`a_(1)= Ralpha=1xx4=4 m//s^(2)`
`a=sqrt(a_(c)^(2)+a_(1)^(2))=4sqrt2 m//s^(2)`