You are at an amusement park inside a very large cylinder (r=10m). The cylinder

Question

You are at an amusement park inside a very large cylinder (r=10m). The cylinder slowly begins spinning with an acceleration of 0.2 radian/s2. As it speeds up you are pressed against the sides of the cylinder and then the floor falls away leaving you suspended against the wall. You feel a horizontal 'force' equivalent to one gravity pushing you against the wall.
a) how fast are you moving?
b)what is your angular velocity?
c)using only angular equations, how long does it take to reach the desired velocity?

Explanation / Answer

The radius of the cylinder, r = 10 m The angular acceleration, = 0.2 rad/s^2 a) During the motion we have mg = mv^2/r From the above we have         v = sqrt(gr) = 9.89 m/s b) We have a relation v = r = v/r = 0.989 rad/sec c) Initial angular velocity, 1 = 0 Final angular velocity, 2 = 0.989 rad/s Angular acceleration, = 0.2 rad/s^2 We have an equation    t = (2 - 1) / = 4.945 sec   

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