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Unformatted text preview: mata (jpm2873) – HW #10 – Antoniewicz – (57420) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Consider the problem of the solid sphere rolling down an incline without slipping. The incline has an angle θ , the sphere’s length up the incline is ℓ , and its height is h . At the beginning, the sphere of mass M and radius R rests on the very top of the incline. M μ ℓ θ h What is the minimum coefficient of friction such that the sphere rolls without slipping? The moment of inertia of a sphere with respect to an axis through its center is 2 5 M R 2 . 1. μ = 5 7 cos θ 2. μ = 5 7 tan θ 3. μ = 3 7 tan θ 4. μ = 2 7 cos θ 5. μ = 3 7 sin θ 6. μ = 2 7 sin θ 7. μ = 2 7 tan θ 8. μ = 3 5 cos θ 002 10.0 points A solid cylinder of mass M = 12 kg, radius R = 0 . 33 m and uniform density is pivoted on a frictionless axle coaxial with its symmetry axis. A particle of mass m = 1 kg and initial velocity v = 18 m / s (perpendicular to the cylinder’s axis) flies too close to the cylinder’s edge, collides with the cylinder and sticks to it. Before the collision, the cylinder was not ro- tating. What is the magnitude of its angular velocity after the collision? Answer in units of rad / s. 003 (part 1 of 2) 5.0 points A student sits on a rotating stool holding two 2 . 2 kg masses. When his arms are extended horizontally, the masses are 0 . 78 m from the axis of rotation, and he rotates with an an- gular velocity of 3 rad / sec. The student then pulls the weights horizontally to a shorter dis- tance 0 . 39 m from the rotation axis and his angular velocity increases to ω 2 ....
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This note was uploaded on 04/07/2011 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.
- Spring '08