Physics Help Forum Calculating centripetal acceleration

 Periodic and Circular Motion Periodic and Circular Motion Physics Help Forum

 Dec 6th 2016, 09:48 AM #1 Junior Member   Join Date: Oct 2016 Posts: 6 Calculating centripetal acceleration When a chainsaw is in operation, the chain moves with a linear speed of v=6.0m/s. At the end of the saw, the chain follows a semicircular path with a radius of r=0.049m. I thought the formula for centripetal acceleration was v^2/r, but apparently that isn't it. Am I unable to use linear speed in the centripetal accel formula?
 Dec 6th 2016, 10:56 AM #2 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,344 You are correct - the magnitude of radial acceleration for a particle moving on a circular course at constant speed is v^2/r. So here the magnitude of acceleration is: $\displaystyle | \vec a | = \frac {v^2} r =\frac {(6 \ \frac m s )^2}{0.049m}\ =\ 735 \frac m {s^2}$ The direction of the acceleration is inwards toward the center of rotation, so in vector form the acceleration is: $\displaystyle \vec a = -735 \hat r \ \frac m {s^2}$ where $\displaystyle \hat r$ is the unit vector in the radial direction. Note the minus sign - could that be what you're missing? Last edited by ChipB; Dec 6th 2016 at 11:04 AM.
 Dec 6th 2016, 12:07 PM #3 Senior Member   Join Date: Jun 2010 Location: NC Posts: 417 Physics does linear kinematics, then circular. Real design requires vector analysis of motion. Vectors are needed. If you know the derivatives of the sine and csine - these Items might make sense to you. 1.25 Vector Basis: Circular Motion | THERMO Spoken Here! Altitude of Geostationary Orbits | THERMO Spoken Here! Just a Thought... JP
 Dec 6th 2016, 12:55 PM #4 Junior Member   Join Date: Oct 2016 Posts: 6 apparently the answer was 3.1*10^5 m/s^2 ... can anyone explain how to get to that answer?
Dec 6th 2016, 02:14 PM   #5
Physics Team

Join Date: Jun 2010
Location: Morristown, NJ USA
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 Originally Posted by ilovephysics apparently the answer was 3.1*10^5 m/s^2 ... can anyone explain how to get to that answer?
I can't explain it. But clearly that answer is wrong - an acceleration of that magnitude is equivalent to 30,000 g's! No chain saw blade could withstand that!

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