Plane Curvilinear Motion - Polar Coordinates - Example 3.4-3

 

Consider the following mechanism consisting of a slotted bar rotating about the fixed point O that is driving pin A which is constrained to move along the horizontal guide shown. Note that θ is the angle made by the slotted bar with a horizontal reference and r is the distance from the fixed point O to the pin A.

 

 

If the slotted bar is rotating counter-clockwise at a decreasing rate, what are the signs of the first two time derivatives of θ and r?

 

(dθ/dt), (d ²θ/dt ²) positive and (dr/dt) negative
(dθ/dt), (dr/dt) positive and (d ²θ/dt ²) negative
(dθ/dt) positive and (dr/dt), (d ²θ/dt ²) negative
(dr/dt), (d ²θ/dt ²) positive and (dθ/dt) negative