A girl on a merry-go-round platform holds a pendulum in her hand. The pendulum i

Question

A girl on a merry-go-round platform holds a pendulum in her hand. The pendulum is 5.3 m from the rotation axis of the platform. The rotational speed of the platform is 0.021 rev/s. It is found that the pendulum hangs at an angle ? to the vertical. Find ?.

A penny is sitting on the edge of an old phonograph disk that is spinning at 33 rpm and has a diameter of 12 inches. What is the minimum coefficient of static friction between the penny and the surface of the disk to ensure that the penny doesn't fly off?

A speedway turn, with radius of curvature R = 340 m, is banked at an angle ? = 45° above the horizontal.
(a) What is the optimal speed at which to take the turn if the track's surface is iced over (that is, if there is very little friction between the tires and the track)?
vzero friction =

(b) If the track surface is ice-free and there is a coefficient of friction µs = 0.76 between the tires and the track, what are the maximum and minimum speeds at which this turn can be taken?
vmin =
vmax =

Explanation / Answer

The angular speed of the disk = 33rpm = 3.45 rad/s

the diameter of the disk d = 12in then radius r = 6in = 0.1524 m

Therefore the minimum coefficient of static firction

               mv^2/r = s mg

therefore

            s = v^2/rg = (r)^2/rg = (0.1524)(3.45)^2 / 9.8

                                                = 0.185

(c) The radius of curvature of the turn r = 340m

the banking angle = 45

then for banking

                tan = v^2/rg

          therefore the optimal speed

                  v = rg tan = (0.1524)(9.8)tan45

                                     = 1.22 m/s

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