Question

Looking to double check my answer/method:
Gear C has radius 0.17 m and rotates with angular velocity -4.3 k rad/s. The connecting link rotates at angular velocity -2.4 k rad/s. Gear D has radius 0.06 m. Find the angular velocity of gear D (in rad/s). Note that gear C is pinned to ground and gear D is a planetary gear. Give a positive response to indicate the rotation direction is counter-clockwise, or a negative response to indicate clockwise rotation.

Answer 1

essentially, I calculated the velocity of the connecting rod at the intersection point 'p'
using v_r = w*r_c = -2.4 rad/s*.17m = -.408m/s
then calculated the velocity of gear C at point 'p'
v_c = -4.3 rad/s * .17m = -.731 m/s

then figured that the relative velocity of gear D compared to point p would be the opposite of the difference between the two velocities
v_d|p = -(-.731 - -.408) = .323 m/s

then converted that into an angular velocity by dividing by the radius of gear D
w_d = v_d|p/r_d = .323/.06 = 5.383 rad/s

I'm wondering if I made a false assumption or anything? I'n not the most confident in my work and would appreciate a proof read