Consider the situation as shown in the figure. The ball attached to a string is moving in the verticle circle find the (a) centripetal acceleration and (b) tanfential acceleration when the string makes an anhle `60^(@)` with lower vertical. Also, express the total acceleration in vector from taking `A` as origin.

Explanation

`h=L-L cos 60^(@)=(L)/(2)`
`v^(2)=u^(2)-2gh=6gL-2G(L0/(2)=5gL`
`a_(c)=(v^(2))/(L)=5g`
`a_(c)=(v^(2))/(L)=5g`
`a_(t)=g sin 60^(@)=(sqrt(3)g)/(2)`
`veca=a_(x)hati+a_(y)hatj`
`=-(a_(c)cos30^(@)+a_(t) cos 60^(@))hati`
`+(a_(c )sin30^(@)-a_(t)sin60^(@))hatj`
`=-(5gxxsqrt(3)/(2)+sqrt(3g)/(2).(1)/(2))hati+(5gxx(1)/(2)-sqrt(3g)/(2)sqrt(3)/(2))hatj`
`=(-11sqrt(3)g)/(4)hati+(7g)/(4)hatj`