A particle moves outward along a spiral. Its trajectory is given by r = A0, where A is a constant. A = (1/n) m/rad. 0 increases in time according to 0 = ať²/2, where a is a constant. (a) Sketch the motion, and indicate the approximate velocity and acceleration at three different points.
A particle moves outward along a spiral. Its trajectory is given by r = A0, where A is a constant. A = (1/n) m/rad. 0 increases in time according to 0 = ať²/2, where a is a constant. (a) Sketch the motion, and indicate the approximate velocity and acceleration at three different points.
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Transcribed Image Text:A particle moves outward along a spiral. Its trajectory is given by r = A0, where A is a constant.
A = (1/n) m/rad. 0 increases in time according to 0 = ať²/2, where a is a constant.
(a) Sketch the motion, and indicate the approximate velocity and acceleration at three different points.
Transcribed Image Text:Hints: a) The trajectory is given, so to sketch velocity and acceleration vectors at three different points
find the velocity and acceleration (for acceleration a see hints given in part b).
v = rî + rô ð and a = (* – ri) î + (rö + 2ré) ð
The components of velocity and acceleration in polar coordinates should give a feeling about magnitude and direction of vectors
v and a as function of position. You do not need to be perfect in the sketch , just give e feeling (i.e., do not calculate) how the
magnitude and direction of these vectors change as function of position . Remember velocity is always in the tangential direction
with the trajectory, which in our case is a spiral one and not a circular one
from the formula of the acceleration in polar coordinates prove that
5a?r
b)
a = (* – rỡ) î + (rë + 2rė) ôð = (ª .
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