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Running around a conical roof
Harry Potter is being chased by a dragon around the conical roof of the Hogwarts tower. The pitch of the tower roof is 20 degrees with respect to the horizontal and Harry can manage a coefficient of friction of .8 with the tiles of the roof. At the point where Harry is clinging to the tower roof the diameter is 12 m. Assuming the case for uniform circular motion what maximum speed can Harry move around on the roof and not slide off at this level without resorting to magic?
Why would there be a maximum speed that Harry can run at?
Customer support service by UserEcho
There are actually two forces involved as he is running around the roof top. One of the forces is due to gravity. The other is due to the affects of centripetal force. Since moving in a circle requires a force towards the center of the circle Harry is moving about, Harry (and his feet) will "feel" something pushing him outwards so that he doesn't actually fall straight toward the center. Although the gravitational force will be constant in a uniform circular motion, the force pushing him outwards will not be uniform because it depends on how fast he is moving (F=mv^2/r).