Determine the collar\'s velocity and acceleration at t = 0s. Please help and sho

Question

Determine the collar's velocity and acceleration at t = 0s. Please help and show all work.

The pin is connected together such that one collar slides over a fixed rod and the other slides over a rotating rod. The geometry in the vicinity of theta = 0degree is approximately r^2 = (4 cos 2that) ft^2. Rod OA starts at rest at 6 = 0degree and accelerates counter-clockwise with an angular acceleration of a = 150/s^2 . Determine the collar's velocity and acceleration at t = 0 s. Use u_r and u_theta notation for both vectors.

Explanation / Answer

A double collar C is pin-connected together such that one collar slides over a fixed rod and the other slides over a rotating rod. If the geometry of the fixed rod for a short distance can be defined by a lemniscate, r2 = (a cos b), determine the collar’s radial and transverse components of velocity and acceleration at the instant = 0° as shown. Rod OA is rotating at a constant rate of '. Given: a 4 ft2= b 2= ' 6 rad s = Solution: 0 deg= r a cos b( )= r2 a cos b( )= 2rr' a b sin b( )'= r' a b sin b( )' 2r = 120 2rr'' 2r'2+ a b2 cos b( ) '2= r'' a b2 cos b( ) '2 2r'2 2r = vr r'= vr 0 ms= v r'= v 12 fts= ar r'' r'2= ar 216 ft s2 = a 2r''= a 0 ft s2

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