Question: When a particle moves in a circle with constant speed, the magnitudes of its position vector and velocity vector are constant. (a) Differentiate rr =
When a particle moves in a circle with constant speed, the magnitudes of its position vector and velocity vector are constant.
(a) Differentiate r·r = r2 = constant with respect to time to show that v·r = 0 and therefore v┴r.
(b) Differentiate v·v = v2 = constant with respect to time and show that a·v = 0 and therefore a┴v. What do the results of (a) and (b) imply about the direction of a?
(c) Differentiate v·r = 0 with respect to time and show that a·r + v2 = 0 and therefore ar = -v2/r.
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a d dt rr r d r dt d r dt r 2 vr 0 Therefore v r b d dt v v ... View full answer
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