Concept explainers
A uniform, solid metal disk of mass 6.50 kg and diameter 24.0 cm hangs in a horizontal plane, supported at its center by a vertical metal wire. You find that it requires a horizontal force of 4.23 N tangent to the rim of the disk to turn it by 3.34°, thus twisting the wire. You now remove this force and release the disk from rest. (a) What is the torsion constant for the metal wire? (b) What are the frequency and period of the torsional oscillations of the disk? (c) Write the equation of motion for θ(t) for the disk.
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
Mastering Physics with Pearson eText -- Standalone Access Card -- for University Physics with Modern Physics (14th Edition)
Additional Science Textbook Solutions
Conceptual Integrated Science
College Physics
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
The Cosmic Perspective (8th Edition)
College Physics (10th Edition)
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
- For each expression, identify the angular frequency , period T, initial phase and amplitude ymax of the oscillation. All values are in SI units. a. y(t) = 0.75 cos (14.5t) b. vy (t) = 0.75 sin (14.5t + /2) c. ay (t) = 14.5 cos (0.75t + /2) 16.3arrow_forwardA watch balance wheel (Fig. P15.25) has a period of oscillation of 0.250 s. The wheel is constructed so that its mass of 20.0 g is concentrated around a rim of radius 0.500 cm. What are (a) the wheels moment of inertia and (b) the torsion constant of the attached spring? Figure P15.23arrow_forwardA nylon siring has mass 5.50 g and length L = 86.0 cm. The lower end is tied to the floor, and the upper end is tied to a small set of wheels through a slot in a track on which the wheels move (Fig. P18.76). The wheels have a mass that is negligible compared with that of the siring, and they roll without friction on the track so that the upper end of the string is essentially free. Figure P18.76 At equilibrium, the string is vertical and motionless. When it is carrying a small-amplilude wave, you may assume the string is always under uniform tension 1.30 N. (a) Find the speed of transverse waves on the siring, (b) The string's vibration possibilities are a set of standing-wave states, each with a node at the fixed bottom end and an antinode at the free top end. Find the node-antinode distances for each of the three simplest states, (c) Find the frequency of each of these states.arrow_forward
- The moment of inertia of a physical pendulum of 3 kg oscillating at small angles around an axis at a distance h = 0.8 m from the center of mass is given as I = 1.2 kg m ^ 2. What should be the length of a simple pendulum with a mass of 0.8 kg oscillating in the same period as the small oscillations of the pendulum? bIf the swing amplitude is 0.5 rad, what is the maximum value of the angular acceleration? (a-10rad/S b-20rad/s c-1/10rad/s d-20rad/S). ( figure for first question)arrow_forwardA solid copper cube has an edge length of 85.5 cm. How much stress must be applied to the cube to reduce the edge length to 85.0 cm? The bulk modulus of copper is 1.4*1011 N/m2.arrow_forwardA 73 m length with a radius of 2.3 m of a cylinder supports a 9.5 x 10 5 kg mass which presses down thecylinder at a modulus of 9.4 x 10 10 N/m 11. What is the downward deflection of the cylinder?arrow_forward
- Consider a “round” rigid body with moment of inertia I = BMR2, where M is the body’s mass, R is the body’s radius, and B (beta) is a constant depending on the type of the body. The center of the “round” rigid body is attached to a spring of force constant k, and then the body is made to roll without slipping on a rough horizontal surface. Due to the spring, it is expected the body will oscillate by rolling back and forth from its resting position. A. Determine the angular frequency and the period for small oscillations of the round rigid body. Express your answers in terms of B (beta). B. Among the four “round” rigid bodies shown at the table, for the same masses and radii, which among them will have the most number of cycles per second.arrow_forwardthe pendulum consists of a uniform disk with radius r = 10.0 cm and mass 500 g attached to a uniform rod with length L = 500 mm and mass 270 g. (a) Calculate the rotational inertia of the pendulum about the pivot point. (b) What is the distance between the pivot point and the center of mass of the pendulum? (c) Calculate the period of oscillation.arrow_forwardA 1.80 kg monkey wrench is pivoted 0.250 m from its center of mass and allowed to swing as a physical pendulum. The period for small-angle oscillations is 0.940 s. (a) What is the moment of inertia of the wrench about an axis through the pivot? (b) If the wrench is initially displaced 0.400 rad from its equilibrium position, what is the angular speed of the wrench as it passes through the equilibrium position?arrow_forward
- A physical pendulum composed of a solid sphere with radius R = 0.500m, is hanged from a ceiling by string of length equal to radius. What are the (a) angular frequency, (b) period, (c) frequency of the system for small angles of oscillation? The moment of inertia of the pendulum about its axis of rotation is I= 2/5 mR^2arrow_forwardA solid copper cube has an edge length of 86.9 cm. How much stress must be applied to the cube to reduce the edge length to 86 cm? The bulk modulus of copper is 1.4 x 1011 N/m2.arrow_forwardConsider a “round” rigid body with moment of inertia I = BMR2, where M is the body’s mass, R is the body’s radius, and B is a constant depending on the type of the body. The center of the “round” rigid body is attached to a spring of force constant k, and then the body is made to roll without slipping on a rough horizontal surface. Due to the spring, it is expected the body will oscillate by rolling back and forth from its resting position. A. Determine the angular frequency and the period for small oscillations of the round rigid body. Express your answer in terms of B. B. Among the four “round” rigid bodies shown at the table, for the same masses and radii, which among them will have the most number of cycles per second.arrow_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning