Rotational Inertia - Introductory Physics - Solved Paper, Exams of Physics

Download Rotational Inertia - Introductory Physics - Solved Paper and more Exams Physics in PDF only on Docsity! Phusies pa ee we Saconseny FAL 2o0- = University of California wt 2002 Department of PI Physics 8A, Fall —- Midterm 2 Second Midterm Exam November 6, 2002 You will be given 100 minutes to work this exam, No books, but you may use a handwritten note sheet no larger than an 8 1/2 by 11 sheet of paper. Your description of the physics involved in a problem is worth significantly more than any numerical answer. Show all work, and take particular care to explain what you are doing. Write your answers directly on the exam, and if you have to use the back of a sheet make sure to put a note on the front. Do not use a blue book or scratch paper. sin 45° = 0.707, cos 45° = 0.707, sin 30° = 0.500, cos 30° = 0,866 Rotational Inertias for radius R or length L: sphere about axis: (2/5)MR2 spherical shell about axis: (2/3)MR2 disk about axis: (1/2)MR2 hoop about axis: MR2 rod about perpendicular at midpoint: ML2/12 + a xyan4R econstent pn SMe on fe of SF ema Z rF m ! Each part is worth the number of points indicated, These should sum to 100 points. Setup and explanation are worth almost all the of the points. Clearly state what you are doing and why. In particular, make sure that you explain what principles and conservation rules you are applying, and how they relate. ‘ a = £ 3 : j I 4 ° DISCUSSION SEC1ION DATE/TIME; _Mion._\-! 5 6 Read the problems carefully. Try to do all the problems. aaial If you get stuck, go on to the next problem. Don't give up! Try to remain relaxed and work steadily. 1A) (2 pts) A ladder leans against a wall. Tf the ladder is not to slip, which one of the following must be true? a) the coefficient of friction between the ladder and the wall must not be zero b) the coefficient of friction between the ladder and the floor must not be zero c) both a and b - d) cithera orb ¢) neither a nor b 1B) (2 pts) Ifa sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is a) 1/5 MR? Bm Zea b) 3/5 MR? ee S c) MR? : ae @ 15 MR? Fee oh nae e) 9/5 MR? rt 1C) (2 pts) We may apply conservation of energy to a cylinder rolling down an incline without slipping, thus saying no work is done by friction, because 4) there is no friction present b) the angular velocity of the center of mass about the point of contact is zero c) the coefficient of kinetic friction is zero ¢d) the linear velocity of the point of contact (relative to the surface) is zero €) the coefficients of static and Kinetic friction are equal in this case 1D) @ pts) A figure skater stands on one spot on the ice (assumed frictionless) and spins around with her arms extended. When she pulls in her arms, she reduces her rotational inertia and her angular speed increases so that her angular momentum is conserved, Compared to her initial rotational kinetic energy, her rotational kinetic energy after she has pulled in her arms must be 1 (a) the same. . b) larger because she's rotating faster. + c) smaller because her rotational inertia is smaller. IE) (2 pts) In simple harmonic motion, the magnitude of the acceleration is greatest when the = — a) velocity is maximum b) displacement is zero c) force is zero d) displacement is maximum e) none of these  4 (20 pts) A 1000 kg car is being lifted by a hydraulic jack. The large piston has radius R=10 cm, and the small piston has radius r=1cm. Hydraulic fluid has about the same density as water. See figure. {ae FE a) What is the pressure at point A? 2 2 | ql i? b) What is the pressure at point B? pe 6 = f os ar prespert pelowaee 6 actattee orm uth (tm) a 1 wd pat (on lps. & 5 atk B J=eFad & h F | z p= f = A AL = Ving . ae aM F - 2\2060 |b 1 3 a Po ; F ot tty tes AA F Pat )  3 (20 pts) A wheel of radius r and mass m would normally: roll down a ramp. In this problem, it's constrained by a string, which prevents it from rolling. What's the tension in the string? ey, pare lle fo Wenp - 2r% Ce Oblate oy wll, 6 (o) 6 (20 pts) A block of mass m is attached to a spring with spring constant k. The mass is sitting at the equilibrium position when it is suddenly hit to add energy E to it. It then oscillates around the equilibrium position with a riod T.” — a) What are the maximum values of the position, velocity and acceleration of this motion? b) Make a sketch showing where in the moti 1/2 of the way through, or whatever) ion those maxima occur. (E.g at the center, = "6 = Lm = lA 1 yt = bee J ave = A= te,