Physics Study Guides.pdf - James M. Hill Memorial High School

PhysicsCircular Motion Problem Guide cont.Mass on a String (cont.)ExampleA 5 g mass at rest is attached to the end of a 1 meter long string. At the top of the path, what speed will the mass bemoving at if it is to just barely make it over?SolutionGiven: m = 5 g, l = 1 mFind: v minbecause we're looking for the minimum speed, T = 0set mg equal to the centripetal forcesolve for v minRolling BodiesIf an object rolls down a ramp, there must be friction. Without friction, the object would slip down the ramp withoutrotating. Because friction causes the object to roll, friction is the force we plug in when we use the torque equation.ExampleA hoop of mass M, radius R, and moment of inertia of MR 2 is released from the top of a ramp of angle θ. What is theacceleration of the center of mass of the hoop? Assume there is no slipping.SolutionGiven: m = M, r = R, I = MR 2 , let μ be the coefficient of static frictionFind: aandfriction is the force providing torqueset the two expressions for torque equal to each otherPulleysIn a pulley system, tension causes the pulley to rotate, which means tension is the force we plug in for torque. If thereare two blocks attached to a single string, we know that they will have the same acceleration because they are in thesame system. Also, if they are of different mass, they will have different free body diagrams, so draw one for each!ExampleA pulley of radius R is connected to a string with 2 blocks of different mass on both side. One block is 3 g and the otheris 6 g. Find the rotational inertia of the pulley.SolutionGiven: m 1 = 6 g, m 2 = 3 g, r = RFind: ISince block 1 is 6 g and block 2 is 3 g, we can conclude that block 1 will fallin this system while block 2 rises.andTo find T 1 and T 2 , use:Page 4 of 4