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Physics 103 Exam IVb 8 December 2010 Name ______________________________ Part A: Select and circle the best answer for each of the following questions: [0 or 1 point each] 1. The time rate of change in angular velocity is defined to be the a) angular acceleration b) angular momentum c) moment of inertia d) angular velocity 2. The angular velocity vector for a spinning rigid body is directed __________, according to the right-hand-rule. a) along the rotational axis b) perpendicular to the rotational axis 3. A pendulum swinging on the Moon would have a frequency _____ one swinging on the Earth. a) smaller than b) the same as c) larger than d) equal to 4. The “correct” plural of pendulum is ________________. a) pendulums b) pendulae c) pendula d) penduluses 5. The SI units of angular torque are _________________. a) kg m2/s b) N m c) N/m d) kg m/s2 Part B: Solve the following problems. Show your work. [0, 1, or 2 each] 6. A simple pendulum swings at a frequency of 5 Hz. How long is the pendulum? 7. What is the magnitude of the torque exerted by the wrench on the nut? 1 8. A force F = 100 N presses a brake pad against the edge of a spinning disk. The axis of rotation is perpendicular to the plane of the disk, through its center. The coefficient of friction between the pad and the disk is = 0.4. The spinning disk has mass of M = 15 kg, a radius of R = 0.5 m, and a moment of inertia I = 15.0 kgm2 . What is the magnitude of the angular acceleration of the disk about its axis of rotation? 9. A 900 kg car drives with constant speed (10 m/s) around a horizontal circle of radius 50 m. What is the car’s angular speed around the center of the circle? 10. A car wheel rolls without sliding at a speed of 3.00 m/s. The mass of the wheel is 5.00 kg and its radius is 0.15 m. Compute the rotational kinetic energy of the wheel. 1 [The moment of inertia of a disk is MR 2 ] 2 2 11. A compact disk starts from rest and accelerates constantly to an angular speed of 300 rev/min (31.4 rad/s), taking t = 2.00 seconds to do so. Compute the angular displacement during this time interval. 12. A particle of mass m = 2.00 kg has a velocity of v = 4.00 m/sec parallel to the x-axis. What is the angular momentum of the particle about the origin when its position is at r = 2.00 m from the origin along a line making a 30o angle with the x-axis? [Including direction!] 13. A hollow sphere begins at rest, at height h, and rolls without slipping down an inclined plane. Use energy conservation to find the speed, v, of the spherical shell at the bottom of the incline. 2 h 2.0m , R 0.5m , M 10kg , I MR 2 3 3 14. An object of unknown mass is attached to an ideal spring with a force constant 100 N/m. The object vibrates on the spring at a frequency of 5.00 Hz. Evaluate the mass of the object. 15. Compute the moment of inertia of this system of three masses, about the z-axis. [M1 = 2 kg; M2 = 4kg; M3 = 1 kg] [ r1 ( 0,0 ); r2 ( 3m,0 ); r3 ( 0,3m ) ] 4 Part C: Work the following problem. Show your work, and use words and phrases to describe your reasoning. [10 points] 16. An ideal string is wrapped around a pulley. Hanging from the free end of the string is a mass, m = 4.0 kg. The axle of the pulley is frictionless, but the string does not slip on the pulley. Calculate the acceleration of 1 the mass, m. M = 10.0 kg and R = 0.5 m and I MR 2 . Don’t forget 2 the free body diagrams. 5 Vectors: A Ax xˆ Ay yˆ Az zˆ A A Ax2 Ay2 Az2 Cx = Ax + Bx Cy = A y + B y A B Ax Bx Ay B y Az Bz AB cos Kinematics: Constant acceleration: 1 2 a aˆ a Cz = Az + Bz A B AB sin r xxˆ yyˆ dr v vx xˆ v y yˆ dt direction by right hand rule dv a ax xˆ a y yˆ dt r rf ri r v t v a t Earth’s gravity: g = 9.8 m/sec2 1 x xo voxt axt 2 2 vx vox axt 2 vx2 vox 2ax x xo vx v f vi 2 Uniform circular motion: ar v2 r Quadratic formula x b b 2 4ac 2a Newton’s 2nd Law Fx = max Friction Ff = N Restoring Force (Hooke’s Law) x xo vx t Fy = may Fs k o Fx kx 6 Fz = maz Work & Energy Mechanical Energy Impulse & Momentum Rocket angular motion constant angular acceleration angular momentum W = Fdcos() K U spring E Wnonconservative I J F t p p mv vector version dv dm Fext m V dt dt dm 0 dt t v a s t t r r r = o + t t Universal Gravitation Fg = o + ot + (1/2)t2 rigid body static equilibrium dv x dm ve , x dt dt 1 I 2 2 Moment of Inertia for a particle about a point: I mr 2 2 o2 2 L I F 0 & dL dt GM m r2 G 6.67 10 11 Fext , x m Kr Lrp torque 1 2 k l l o 2 1 kx 2 2 No external force : p final pinitial one dimensional as in the text dm ve 0 ; 0 dt 1 2 mv 2 U spring E=K+U kinetic energy 1 K I 2 2 r F Simple Harmonic Motion Wtotal = K; Wconservative = -U Ug = mgy or U mgh Ug GM m r ve 2GM R N m2 kg 2 x A cos t 2f spring: 7 k m pendulum: g 0 Waves y A coskx t k 8 2 2 f wave speed: c f