A ring rotates about z axis as shown in figure. The plane of rotation is xy. At a certain instant the acceleration of a particle P (shown in figure) on the ring is `(6 hat i – 8 hat j)" m/s"^(2)`. Find the angular acceleration of the ring & the angular velocity at that instant. Radius of the ring is 2m.

Answer

`-3hat(k) rad//s^(2), -2hat(k) rad//s`

Explanation

`vec(a_(1))=6hat(i)=vec(alpha)xxvec(R)=vec(alpha)xx2hat(j)rArr vec(alpha)=-3hat(k) rad//s^(2)`
`vec(a_(r))=-8hat(j)=vec(omega)xxvec(v)=vec(omega)xx(omegaR)hat(i) rArr vec(omega)=-2hat(k) rad//s`