Span Classsearchtermclassspan Room Notes On Uniplanar Kinematics

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Span Classsearchtermclassspan Room Notes On Uniplanar Kinematics
Irving Stringham
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5 Problems. Verify the following formulae for the deter- mination of velocity and acceleration.
(i). If a point move with speed v in the curve y =. F(x}, represented in Cartesian co-ordinates, prove that its velocity is dp v_[i_ *'/'(>-)] dt ~~ I/ i + [/''OrT]' (2). If a point move with velocity v in the curve r =f(ff), represented in polar co-ordinates, prove that its velocity is (3). If v = speed, and R == radius of curvature, prove that the tensor of acceleration is dv dt ) In the following
...curves let s length of curve, = vectorial angle, x = abscissa in a Cartesian system. If in each a point move with speed v, determine the expressions for velocity, acceleration, and radius of curvature.
(4. ) p = j/V -(- $* -f- ia sinh -.
dp _ v (s -f- z) fl? 2 /o _ v 2 (a 1 ias} (5) P = a e cis ^, the equiangular spiral.
dp v (i -(- m) -. - - cis P.
"^ I/ i + w z (6). P^ cis B, the spiral of Archimedes.
(?) Pz~ c i s ^' the reciprocal spiral.
(8). P = x -+- z'a^*", the logarithmic curve.
x (9). P = x -\- zVcosh, the catenary.


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