Question

The device shown rotates about the fixed z-axis with angular velocity ω = 18 rad/s and angular acceleration α = 36 rad/s² in the directions indicated. Determine the instantaneous velocity and acceleration of point B.

B 50° 50° Ο Α هلال α OA = 380 mm, AB = 650 mm Answers: VB -14.361 -0.79782 -0.49794 + + Uk) m/s X ав = 28.721 -258.49 18 Ji + + Uk) m/s2

Answer 1

Distance of the point B from z-axis will be

OA + ABcos50 = 0.797812

Now, the velocity will be in tangential direction at the point B and from the figure you can see it will be directed in negative x-axis so

v_B = -0.0.797812 x 18 = -14.361i m/s

So the other components will be zero for the velocity at point B.

Now for the acceleration, there will be two types or say in two directions first radial along the towards the radial distance from point B which is the negative y direction and the other will be tangential acceleration directed in positive x direction. So there won't be any acceleration in z direction. So the result you have calculated is correct for i and j directions but for the k it will be zero.