Unit Dynamics Module The Dynamics of Circular Motion page 1 of 1 Solving Circular Motion Problems When solving problems any criterion for which the normal force is negative violates the equations of uniform circular motion The minimum speed with which a bucket full of water must rotate so that the water remains in the bucket is v gR The maximum speed that a ferris wheel can rotate so that the passengers remain seated on the ride in the absence of seatbelts is v gR A bucket of water is in uniform circular motion with radius R You would like to know the speed required so that the water doesn t fall out of the bucket Focus on a parcel of water in the bucket when the bucket is upside down The contact force on the water by the bucket is centripetal or in the downward direction The weight of the parcel of water is also in the downward direction Choose up as the positive direction The right side of Newton s second law is the product of the mass of the parcel of water and its acceleration with magnitude v 2 R in the downward direction Solve for the normal force If the normal force is negative the water will not be in uniform circular motion so m v 2 R mg must be greater than zero The minimum speed with which a bucket full of water must rotate so that the water remains in the bucket is v gR A ferris wheel with radius R is in uniform circular motion You would like to know the maximum speed that the ferris wheel can rotate so that a person without a seatbelt will stay on the ride Focus on a person at the top of the ride There are two forces weight in the downward direction and the contact force in the upward direction The right hand side of Newton s second law is the product of the person s mass and acceleration which is in the downward or negative direction Solve for the normal force If the normal force is negative the person will not be in circular motion and will fly off the ride so mg mv 2 R must be greater than zero The maximum speed that a ferris wheel can rotate so that the passenger remains seated on the ride is v gR www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1924 doc rev 03 27 2001
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