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Unformatted text preview: r r θ Φ θ θ 34 29 θ v Φ 9° 11.3° + 11.3 Φ + 11.3 Φ 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 ∆ θ a = 2vcos /(r /v) θ Φ a = 2v 2 cos( /2 – /2)/(r ) π Φ Φ cos( /2 – /2) = cos( /2)cos( /2) + sin( /2)sin( /2) = π Φ π Φ Φ π sin( /2) Φ a = 2v 2 /(r ) Φ ∙ ( /2) Φ 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) Φ becomes /2 Φ 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, Φ the angles between them must be zero in the picture below) is /2 Φ ....
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- Fall '09
- Acceleration, Quadratic equation, Trigraph, Elementary algebra, P. Henry