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 (6i^−8j^) m/s2. Find the magnitudes of angular acceleration of the ring and its angular velocity at that instant. Radius of the ring is 2m.

at=−8 m/s2 ; ac=+6 m/s2at=rα=8 ; ac=rω2=6α=82=4 rad/s2 ; ω=62=3 rad/s

at=−8 m/s2 ; ac=+6 m/s2at=rα=8 ; ac=rω2=6α=82=4 rad/s2 ; ω=62=3 rad/s

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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 magnitudes of angular acceleration of the ring and its angular velocity at that instant. Radius of the ring is 2m.

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$5 rad / s^{2}, \sqrt{5} rad / s$

$3 rad / s^{2}, 2 rad / s$

$4 rad / s^{2}, \sqrt{3} rad / s$

$2 rad / s^{2}, 3 rad / s$

answer is A.

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$a_{t} = - 8 {m/s}^{2}; a_{c} = + 6 {m/s}^{2}$

$a_{t} = rα = 8; a_{c} = {rω}^{2} = 6$

$α = \frac{8}{2} = 4 rad / s^{2}; ω = \sqrt{\frac{6}{2}} = \sqrt{3} rad / s$

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