PhysI_09222009 - r r 34 29 v 9 11.3 + 11.3 + 11.3 11.3 3.44...

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Unformatted text preview: r r 34 29 v 9 11.3 + 11.3 + 11.3 11.3 3.44 m 50 m T m M t R r 09-22-2009 171.101, General Physics for Physical Science Majors I From the last lesson, we learned that in uniform circular motion, acceleration is found using the equation a = v 2 /r, and we gathered this equation through the following steps: v = 2vcos a = 2vcos /(r /v) a = 2v 2 cos( /2 /2)/(r ) cos( /2 /2) = cos( /2)cos( /2) + sin( /2)sin( /2) = sin( /2) a = 2v 2 /(r ) ( /2) a = v 2 /r BUT: Because the velocity is counter-clockwise, the acceleration is in the NEGATIVE direction. SO: a = -v 2 /r (in the case of the moon orbiting Earth) P. Henry noted today that the reason sin( /2) becomes /2 from the third to fourth step is that the limit of the entire equation as approaches zero (recall that for an infinite number of lines, the angles between them must be zero in the picture below) is /2 ....
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PhysI_09222009 - r r 34 29 v 9 11.3 + 11.3 + 11.3 11.3 3.44...

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