Concept explainers
A three-blade wind turbine used for research is supported on a shaft so that it is free to rotate about O. One technique to determine the centroidal mass moment of inertia of an object is to place a known weight at a known distance from the axis of rotation and to measure the frequency of oscillations after releasing it from rest with a small initial angle. In this case, a weight of Wadd = 50 lb is attached to one of the blades at a distance R = 20 ft from the axis of rotation. Knowing that when the blade with the added weight is displaced slightly from the vertical axis, and the system is found to have a period of 7.6 s, determine the centroidal mass moment of inertia of the three-blade rotor.
Fig. P19.46
Want to see the full answer?
Check out a sample textbook solutionChapter 19 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- Ex. A vehicle wheel, tire and suspension assembly can be modeled crudely as a single degree of freedom spring mass system. The mass of the assembly is measured to be about 300kg. its frequency of oscillation is observed to be π rad/sec. What is the approximate stiffness of the tire, wheel and suspension assembly? ilippines) Accessibility: Investigatearrow_forwardMaximum fluctuation of kinetic energy in an engine has been calculated to be 2600 J. Assuming that the engine runs at an average speed of 200 rpm, the polar mass moment of inertia (in kg.m2) of a flywheel to keep the speed fluctuation within +0.5% of the average speed isarrow_forwardQ.6 Find the equivalent spring constant and equivalent mass of the system shown below with reference to x1. Also, find the natural frequency. Assume that the bar AOB is rigid with mass m3 and mass moment of inertia Jo about point O. The spring attached to the mass at A has a mass m; and the other springs are of negligible mass. Take mi = m/4. 21 1.51 B m m k msarrow_forward
- Determine the fundamental natural frequency of the spring mass system shown in Fig.1 using (i) Dunkerley’s method and (ii) Matrix iteration method (only 2 iterations).arrow_forward1. The figure shows a uniform rod with a mass of 3 kg and is pivoted at point A. There is a solid mass of 4 kg at point C. The value of the coefficient of elasticity of the spring k1 = 20 kN / m and k2 = 100 kN / m. Determine; a) the natural system Frequency b) The time taken by the system to complete one oscillating. 20 cm 80 cm k1 B k2 k2 k2arrow_forwardConsider the system shown below. Answer Questions 6-11 based on this figure. How many degrees-of-freedom does the system shown below has? The two pulleys have the identical mass, radius, and the moment of inertia. т, 1, R k т, 1, R Variables x: vertical position of the moving pulley 8: rotation of the moving pulley p: rotation of the fixed pulley m: pulley mass R: pulley radius I: mass moment of the pulley about its own center of mass. k: spring stiffness T: cable tension Assumptions 1. x = 0, 0 = 0, and o = 0 when the spring is undeformed. 2. The cables and springs have negligible mass. 3. There is no slip between the pulley and the cable. 4. Only two-dimensional planar motion is allowed.arrow_forward
- The figure below shows a cylinder floating upright in a fluid. When the cylinderis displaced slightly along it’s vertical axis it will oscillate about it’s equilibriumposition with frequency, ω. Assume that this frequency is a function of thediameter, D, the mass of the cylinder, m, and the specific weight, γ, of theliquid.1. Determine, using the Buckingham Pi Method, how the frequency is relatedto these variables.2. If the mass of the cylinder were increased, would the frequency increaseor decrease?arrow_forwardA submarine is rolling under seawater whose radius of gyration is 12 m and period of oscillation of rolling of ship is 22 seconds then nearest metacentric height in metres isarrow_forwardQuestion 9: Figure 3 shows a mechanical system. The rod (with moment of inertia J) rotates about the pivot at only small rotation angles. As pictured, theta is positive clockwise. Attached is mass m, which moves positive to the right. When stationary in the position shown, all springs are undeflected. Using BOBODDY, find the mathematical model of this system assuming small rotation angle 0. Link, moment of inertia J k3 L₁ 12 5 Ꮎ wwww Figure 3: Mechanical System m k₂ barrow_forward
- Figure shows a mechanical system. The connecting link has moment of inertia J about its pivot point, and rotation angle is positive clockwise. Position of mass m is positive to the right. Both the angular and translational displacements are measured from the equilibrium position where all springs are undeflected. Derive the mathematical model of this system assuming small rotation angle 8. Link, moment. of inertia J L k₁ www m O k₂ wwwarrow_forwardFind the set of initial conditions such that each mass oscillates: a) at the first natural frequency; b) at the second natural frequency;arrow_forwardA 0.1 kg object oscillates as a simple harmonic motion along the x-axis with a frequency f = 3.185 Hz. At a position x1, the object has a kinetic energy of 0.7 J and a potential energy 0.3 J. What tge amplitude of oscillationarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY