My Math Forum circular motion (hard)

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 April 14th, 2011, 06:13 AM #1 Senior Member   Joined: Dec 2010 Posts: 233 Thanks: 0 circular motion (hard) 1.An astronaut is rotated in a horizontal centrifuge at a radius of 5.0m. a)what is the astronaut's speed if the centripetal acceleration has a magnitude of 7.0g? b)How many revolutions per minutes are required to produce his acceleration? c)What is the period of the motion 2.A carnival merry-go around rotates around a vertical axis a constant rate.A passenger standing on the edge of the merry-go-round has a constant speed of 3.66 ms^-1.For each of the following instantaneous situations,state how far the passenger is from the centre of the merry-go-around and in which direction a)the passenger has an acceleration of 1.83 ms^-2 ,east b)the passenger has an acceleration of 1.83 ms^-2,south Please show me the formula and solve the question step by step.if possible,can you show me a image about the question that can makes me understand better,Thank you.i really need help.
 April 14th, 2011, 08:54 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs Re: circular motion (hard) 1.) r = 5.0 m a) $a_r=\frac{v^2}{r}\:\therefore\v|=\sqrt{r\cdot a_r}=\sqrt{$$5.0\text{ m}$$$$7\cdot9.81\text{ \frac{m}{s^2}}$$}\approx18.53\text{ \frac{m}{s}}" /> b) $v=r\omega\:\therefore\:\omega=\frac{v}{r}=\frac{\s qrt{r\cdot a_r}}{r}=\sqrt{\frac{a_r}{r}}=\sqrt{\frac{7\cdot9. 81\text{ \frac{m}{s^2}}}{5.0\text{ m}}}\approx$ $3.71\text{ \frac{rad}{s}}\cdot\frac{60\text{ s}}{1\text{ min}}\cdot\frac{1\text{ rev}}{2\pi\text{ rad}}\approx35.4\text{ rpm}$ c) $T=\frac{2\pi}{\omega}=\frac{2\pi}{\sqrt{\frac{a_r} {r}}}=2\pi\sqrt{\frac{r}{a_r}}=2\pi\sqrt{\frac{5.0 \text{ m}}{7\cdot9.81\text{ \frac{m}{s^2}}}}\approx1.70\text{ s}$ 2.) There isn't enough information given. We need either the angular velocity (or the period), the radius of the merry-go-round, or the centripetal acceleration at the edge.

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# astronaut træning centrifuge

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