* A thin rod of length L and mass m rotates around an axis perpendicular to the rod. passing through the rod’s left end Treat the rod as an object made up of five rods of length L/5. Derive an expression for the rotational inertia of this five-piece object around the same axis, assuming each piece is a point-like object with mass m/5. Compare your result with the expression for the rotational inertia of the one-piece rod
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
College Physics
Additional Science Textbook Solutions
The Cosmic Perspective
Introduction to Electrodynamics
Conceptual Physics (12th Edition)
College Physics: A Strategic Approach (3rd Edition)
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Physics for Scientists and Engineers with Modern Physics
- The moment of inertia of a long rod spun around an axis through one end perpendicular to its length is ML2/3 Why is this moment of inertia greater than it would be if you spun a point mass M at the location of the center of mass of the rod (at L/2)? (That would be ML2/4.)arrow_forwardReview. A piece of putty is initially located at point A on the rim of a grinding wheel rotating at constant angular speed about a horizontal axis. The putty is dislodged from point A when the diameter through A is horizontal. It then rises vertically and returns to A at the instant the wheel completes one revolution. From this information, we wish to find the speed v of the putty when it leaves the wheel and the force holding it to the wheel. (a) What analysis model is appropriate for the motion of the putty as it rises and falls? (b) Use this model to find a symbolic expression for the time interval between when the putty leaves point A and when it arrives back at A, in terms of v and g. (c) What is the appropriate analysis model to describe point A on the wheel? (d) Find the period of the motion of point A in terms of the tangential speed v and the radius R of the wheel. (e) Set the time interval from part (b) equal to the period from part (d) and solve for the speed v of the putty as it leaves the wheel. (f) If the mass of the putty is m, what is the magnitude of the force that held it to the wheel before it was released?arrow_forwardFour objectsa hoop, a solid cylinder, a solid sphere, and a thin, spherical shelleach have a mass of 4.80 kg and a radius of 0.230 m. (a) Find the moment of inertia for each object as it rotates about the axes shown in Table 8.1. (b) Suppose each object is rolled down a ramp. Rank the translational speed of each object from highest to lowest, (c) Rank the objects rotational kinetic energies from highest to lowest as the objects roll down the ramp.arrow_forward
- A competitive diver leaves the diving board and falls toward the water with her body straight and rotating slowly. She pulls her arms and legs into a tight tuck position. What happens to her rotational kinetic energy? (a) It increases. (b) It decreases. (c) It stays the same. (d) It is impossible to determine.arrow_forwardWhile punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.75kg-m2 and its rotational kinetic energy is 175 J. (a) What is the angular velocity of the leg? (b) What is the velocity of tip of the punter's shoe if it is 1.05 m from the hip joint? (c) Explain how the football can be given a velocity greater than the tip of the shoe (necessary for a decent kick distance).arrow_forwardUnreasonable Results An advertisement claims that an 800-kg car is aided by its 20.0-kg flywheel, which can accelerate the car from rest to a speed of 30.0 m/s. The flywheel is a disk with a 0.150-m radius. (a) Calculate the angular velocity the flywheel must have if 95.0% of its rotational energy is used to get the car up to speed. (b) What is unreasonable about the result? (c) Which premise is unreasonable or which premises are inconsistent?arrow_forward
- An electric sander consisting of a rotating disk of mass 0.7 kg and radius 10 cm rotates at 15 rev/sec. When applied to a rough wooden wall the rotation rate decreases by 20 . (a) What is the final rotational kinetic energy of the rotating disk? (a) How much has its rotational kinetic energy decreased?arrow_forwardConsider two objects with m1 m2 connected by a light string that passes over a pulley having a moment of inertia of I about its axis of rotation as shown in Figure P10.28. The string does not slip on the pulley or stretch. The pulley turns without friction. The two objects are released from rest separated by a vertical distance 2h. (a) Use the principle of conservation of energy to find the translational speeds of the objects as they pass each other. (b) Find the angular speed of the pulley at this time. Figure P10.28arrow_forwardUnreasonable Results A gymnast doing a forward flip lands on the mat and exerts a 500- Nm torque to slow and then reverse her angular velocity. Her initial angular velocity is 10.0 rad/s, and her moment of inertia is 0.050kgm2. (a) What time is required for her to exactly reverse her spin? (b) What is unreasonable about the result? (c) Which premises are unreasonable or inconsistent?arrow_forward
- Review. As shown in Figure P10.77, two blocks are connected by a string of negligible mass passing over a pulley of radius r= 0.250 m and moment of inertia I. The block on the frictionless incline is moving with a constant acceleration of magnitude a = 2.00 m/s2. From this information, we wish to find the moment of inertia of the pulley. (a) What analysis model is appropriate for the blocks? (b) What analysis model is appropriate for the pulley? (c) From the analysis model in part (a), find the tension T1(d) Similarly, find the tension T2. (e) From the analysis model in part (b), find a symbolic expression for the moment of inertia of the pulley in terms of the tensions T1 and T2. the pulley radius r, and the acceleration a. (f) Find the numerical value of the moment of inertia of the pulley.arrow_forwardTwo forces F1 and F2 act along the two sides of an equilateral triangle as shown in Figure P11.5. Point O is the intersection of the altitudes of the triangle. (a) Find the magnitude of a third force F3 to be applied at B and along BC that will make the total torque zero about the point O. (b) What If? Will the total torque change if F3 is applied not at B but at any other point along BC? Figure P11.5arrow_forwardConsider the 12.0 kg motorcycle wheel shown in Figure 10.38. Assume it to be approximately an annular ring with an inner radius of 0.280 m and an outer radius of 0.330 m. The motorcycle is on its center stand, so that the wheel can spin freely. (a) If the drive chain exerts a force of 2200 N at a radius of 5.00 cm, what is the angular acceleration of the wheel? (b) What is the tangential acceleration of a point on the outer edge of the tire? (c) How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s? Figure 10.38 A motorcycle wheel has a moment of inertia approximatelyarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning