The design of the rotating arm OA of a control mechanism requires that it rotate about the vertical Z axis at the constant rate rad s Simultaneously, OA oscillates according to 0 sin 4t, where 0 6 radians and t is in seconds measured from the time when 0 Determine the angular velocity w and the ang...

a When t 12 s the angular velocity w 40 cos 4t 46 cos 42 32 rads b When t 18 s the angular veloci ...

The design of the rotating arm OA of a control mechanism requires that it rotate about the

Question:

The design of the rotating arm OA of a control mechanism requires that it rotate about the vertical Z-axis at the constant rate Ω = β˙ = π rad/s. Simultaneously, OA oscillates according to θ = θ₀ sin 4Ωt, where θ₀ = π/6 radians and t is in seconds measured from the time when β = 0. Determine the angular velocity w and the angular acceleration a of OA for the instant

(a) When t = 1/2 s

(b) When t = 1/8 s. The x-y reference axes rotate in the X-Y plane with the angular velocity Ω.