Question

(a) Derive an equation for the radial acceleration that includes v and Cd, but not r. (b) You are designing a merry-go-round for which a point on the rim will have a radial acceleration of 0.500 m/s2 when the tangential velocity of that point has magnitude 2.00 m/s. What angular velocity is required to achieve these values?

          (a) Derive an equation for the radial acceleration that includes v and Cd, but not r. (b) You are designing a merry-go-round for which a point on the rim will have a radial acceleration of 0.500 m/s2 when the tangential velocity of that point has magnitude 2.00 m/s. What angular velocity is required to achieve these values?
        
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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(a) Derive an equation for the radial acceleration that includes v and Cd, but not r. (b) You are designing a merry-go-round for which a point on the rim will have a radial acceleration of 0.500 m/s2 when the tangential velocity of that point has magnitude 2.00 m/s. What angular velocity is required to achieve these values?
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Transcript

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00:01 All right, so let's say we have a merry -go -round, and we want a point on the rim to have a total acceleration of 0 .5 meters per second squared when it has a velocity of 2 meters a second.
00:14 So we want to know what angular velocity is required for this.
00:18 So the total acceleration, we'll write this.
00:21 This will be our tangential acceleration squared plus our radial acceleration squared.
00:26 And so this will be our angular acceleration squared times the radius squared plus omega to the fourth times r squared.
00:37 And so if we're looking for the case where a t is 0 because alpha is 0, then what we'll have is basically a is omega squared times r.
00:49 And we can write r as omega divided by v...
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