Concept explainers
When an object is rolling without slipping, the rolling friction force is much less than the friction force when the object is sliding: a silver dollar will roll on its edge much farther than it will slide on its flat side (sec Section 5.3). When an object is rolling without slipping on a horizontal surface, we can approximate the friction force to be zero, so that ax and αz are approximately zero and vx and ωz. are approximately constant. Rolling without slipping means vx = rωz and αx= rαz. If an object is set in motion on a surface without these equalities, sliding (kinetic) friction will act on the object as it slips until rolling without slipping is established. A solid cylinder with mass M and radius R, rotating with angular speed ω0 about an axis through its center, is set on a horizontal surface for which the kinetic friction coefficient is μk.(a) Draw a free-body diagram for the cylinder on the surface. Think carefully about the direction of the kinetic friction force on the cylinder. Calculate the accelerations ax of the center of mass and αz of rotation about the center of mass, (b) The cylinder is initially slipping completely, so initially ωz = ω0 but vx = 0. Rolling without slipping sets in when vx = rωz. Calculate the distance the cylinder rolls before slipping stops, (c) Calculate the work done by the friction force on the cylinder as it moves from where it was set down to where it begins to roll without slipping.
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
University Physics with Modern Physics, Books a la Carte Edition; Modified MasteringPhysics with Pearson eText -- ValuePack Access Card -- for ... eText -- Valuepack Access Card (14th Edition)
Additional Science Textbook Solutions
Modern Physics
Glencoe Physical Science 2012 Student Edition (Glencoe Science) (McGraw-Hill Education)
An Introduction to Thermal Physics
Physics (5th Edition)
Conceptual Physics (12th Edition)
The Cosmic Perspective Fundamentals (2nd Edition)
- Luis uses a 20-cm-long wrench to tighten a nut, turning it clockwise. The wrench handle is tilted 30° above the horizontal, and Luis pulls straight down on the end with a force of 100 N. How much torque does Luis exert on the nut?arrow_forwardA 1.7 kgkg , 20-cmcm-diameter turntable rotates at 140 rpmrpm on frictionless bearings. Two 450 gg blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is the turntable's angular velocity, in rpmrpm, just after this event? Express your answer to two significant figures and include the appropriate units.arrow_forwardPlease answer vertically, not horizontally so that no steps are miscalculated for this problem. A unicorn is standing on a rotating platform so that it can be admired from every angle. The platform is 5 m in radius and rotates every 8 seconds (otherwise known as 1/8 of a rotation per second). What coefficient of friction must the unicorn's hooves have to keep him from slipping over the edge? This answer is not shown correctly on bartleby. Would he need a higher or lower coefficient of friction to stand closer to the center of the rotating platform? Explain.arrow_forward
- Two big bugs, Buzz and Crunchy each of mass 0.65 kg, are siting on a spinning disk on a horizontal plane. Buzz is sitting halfway and Crunchy is sitting at the outer edge as shown. The radius of the disk is 3 m and it rotates once every 1.2 s. What is the magnitude of the net force on Buzz, in Newtons? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.arrow_forwardA 65 kg student is in a car traveling at 25 m/s on a hill of radius 110 m. When the car is at the top of the hill, what upward force does the seat exert on the student? A 4.2 m long uniform post is supported by a cable having a tension of 1 700 N. What is the mass of this post?arrow_forwardAn engine flywheel initially rotates counterclockwise at 6.83 rotations/s. Then, during 25.1 s, its rotation rate changes to 2.19 rotations/s clockwise. Find the flywheel's average angular acceleration (including its sign) in radians per second squared. Define counterclockwise rotation as positive. what is the average angular acceleration?arrow_forward
- You have a horizontal grindstone (a disk) that is 95 kg, has a 0.36 m radius, is turning at 86 rpm (in the positive direction), and you press a steel axe against the edge with a force of 24 N in the radial direction. 1)Assuming that the kinetic coefficient of friction between steel and stone is 0.20, calculate the angular acceleration of the grindstone in rad/s2. 2)What is the number of turns, N, that the stone will make before coming to rest?arrow_forwardOnly answer part d, e and f. Answers to a, b and c are given. I have two disks. I know that disk A has a mass per unit area σ given by σ = 5r2 and disk B has σ = 3r3. Each disk has radius 10cm. I have a slope at angle 45 degrees to the horizontal that is 2 m long. I time with a stop watch how long it takes the disks to roll down the slope without slipping. (Assuming that the disk’s are let go with zero velocity at the top of the slope). a) Calculate the mass of each disk. Answer: Ma=7.85×10-4kg Mb=3.76×10-5kg b) Calculate the moment of inertia each disk. Answer: Ia= 5.23×10-6kgm2 Ib= 2.69×10-7kgm2 c) Calculate the acceleration down the slope for both disks. Answer: aA=4.16 aB=4.04 d) Calculate the time it takes for each disk to roll. e) What is the total kinetic energy for each disk at the end of the slope? f) At the end of the slope, a fly on the very edge of disk A walks towards the center of the disk at a speed of 1cm/s. What Coriolis acceleration is felt by the fly as it sets…arrow_forwardIn experiment 10, a group of students experimentally measured the rotational inertia of a hoop obtaining 4.55x10-4 kg m2 . What is the percent difference if the mass of the hoop is 0.467 kg and the inner and outer radii are 0.0265 m and 0.03765 m, respectively.arrow_forward
- A variation of the amusement park ride discussed in Problem 11 is the Gravitron, which consists of a rotating cylinder, where riders stand with their backs against the inner surface of the cylinder (see image). As the cylinder rotates faster, riders get stuck to the wall. The effect is great enough, that in some rides, the floor even drops away. Let’s model the Gravitron as a rotating cylinder with vertical walls. The radius of the cylinder is 5.5 m. At one point during the ride, the speed of the Gravitron is 24 rpm, at which point a rider slides down the wall at constant speed. What is the coefficient of kinetic friction between the rider and the wall?arrow_forwardA wind turbine has 12,000 kg blades that are 39 m long. The blades spin at 23 rpm .If we model a blade as a point mass at the midpoint of the blade, what is the inward force necessary to provide each blade's centripetal acceleration?Express your answer to two significant figures and include the appropriate units.arrow_forwardA cat rides a bike 1km. The wheels of the bike have a radius equal to 10cm. What is the total angle the tires rotate through during the cats ride?arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON