In polar coordinates, we have the unit vectors in the direction of and normal to as e, = cos 07 + sin 07, eo = -sin 07 + cos 07, and the unit vectors and in terms of e, and es are 7= cos 0e, - since. 7 = sin de, + cos de.. If F=rcos 0i+r sin 07, show that 2.1 the velocity is given by 2.2 the acceleration is given by ü=re, + roeo, a = (-r0²)e, + (rö +2r0)eo.

Trigonometry (MindTap Course List)
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ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
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Chapter3: Radian Measure
Section3.5: Velocities
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In polar coordinates, we have the unit vectors in the direction of and normal to as
e, = cos 07 + sin 07,
€ = sin 07 + cos 07,
and the unit vectors i and in terms of e, and e, are
i= cos 0e, - sin 0eo,
7 = sin fe, + cos leg.
If r = r cos 0i+r sin 0j, show that
2.1 the velocity is given by
2.2 the acceleration is given by
v=re, + roes,
a= (Fr0²)e, + (rö +2r0)eo.
NB: * = ² and x = d.
00
Transcribed Image Text:In polar coordinates, we have the unit vectors in the direction of and normal to as e, = cos 07 + sin 07, € = sin 07 + cos 07, and the unit vectors i and in terms of e, and e, are i= cos 0e, - sin 0eo, 7 = sin fe, + cos leg. If r = r cos 0i+r sin 0j, show that 2.1 the velocity is given by 2.2 the acceleration is given by v=re, + roes, a= (Fr0²)e, + (rö +2r0)eo. NB: * = ² and x = d. 00
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