Question
S1. A small bead of mass, m , slides freely inside a smooth tube with length 2L . The tube is spun about its center
S1. A small bead of mass,
m
, slides freely inside a smooth tube with\ length
2L
. The tube is spun about its center with constant angular\ speed,
\\\\theta ^()
. Imagine that with the tube spinning, the bead is placed at\ its center and given an initial velocity of
v_(O)
along the tube.\ (a) Write down Newton's laws in polar coordinates and use them to\ find the radial position of the bead as a function of time.\ (b) Suppose that the bead exits the tube after it completes exactly one\ rotation. Find the velocity of the exiting bead,
vec(v)
, expressed in terms\ of its radial and tangential components. Note: You may simplify your\ response by using the identity
e^(x)+e^(-x)=2coshx
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