* Flywheel energy Engineers at the University of Texas at Austin are developing an Advanced Locomotive Propulsion System that uses a gas turbine and perhaps the largest high-speed flywheel in the world in terms of the energy it can store. The flywheel can store
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- The motion of spinning a hula hoop around one's hips can bemodeled as a hoop rotating around an axis not through the center, but offset from the center by an amount h, where h is lessthan R, the radius of the hoop. Suppose Maria spins a hula hoopwith a mass of 0.75 kg and a radius of 0.62 m around her waist.The rotation axis is perpendicular to the plane of the hoop, butapproximately 0.40 m from the center of the hoop. a. What isthe rotational inertia of the hoop in this case? b. If the hula hoopis rotating with an angular speed of 13.7 rad/s, what is its rotational kinetic energy?arrow_forwardA cam of mass M is in the shape of a circular disk of diameter 2R with an off-center circular hole of diameter R is mounted on a uniform cylindrical shaft whose diameter matches that of the hole (Fig. P1 3.78). a. What is the rotational inertia of the cam and shaft around the axis of the shaft? b. What is the rotational kinetic energy of the cam and shaft if the system rotates with angular speed around this axis?arrow_forwardProblems 62 and 63 are paired. 62. C A disk is rotating around a fixed axis that passes through its center and is perpendicular to the face of the disk. Consider a point on the rim of the disk (point R) and another point halfway between the center and the rim (point H) at one particular instant. a. How does the angular speed v of the disk at point H compare with the angular speed of the disk at point R? b. How does the tangential speed of the disk at point H compare with the tangential speed of the disk at point R? c. Suppose we pick a point H on the disk at random (by throwing a dart, for example), and we compare the speeds at that point with the speeds at point R. How will the answers to parts (a) and (b) be different? Explain.arrow_forward
- A lawn mower has a flat, rod-shaped steel blade that rotates about its center. The mass of the blade is 0.65 kg and its length is 0.55 m. You may want to review (Pages 314 - 318). Part A What is the rotational energy of the blade at its operating angular speed of 3460 rpm ? Express your answer using two significant figures. Kr= Submit Part B v Templates Symbols undo redo reset keyboard shortcuts help y = Request Answer If all of the rotational kinetic energy of the blade could be converted to gravitational potential energy, to what height would the blade rise? Express your answer using two significant figures. J Templates Symbols undo redo reset keyboard shortcuts help marrow_forward**** **** 30 Q3. A car has a 750-kg body, four 20-kg wheels, and a 70-kg driver. The wheels are 1 m in diameter and have a radius of gyration k = 0.5 m. What will be the speed of the car if it moves from rest down a 30° plane for a distance of 98 m? Neglect any drag. (g = 10 m/s?) ** **arrow_forward*Chapter 11, Problem 13 Nonuniform ball. In the figure, a ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.47 m. The initial height of the ball is h = 0.34 m. At the loop bottom, the magnitude of the normal force on the ball is 1.92Mg. The ball consists of an outer spherical shell (of a certain uniform density) that is glued to a central sphere (of a different uniform density). The rotational inertia of the ball can be expressed in the general form I = BMR², but B is not 0.4 as it is for a ball of uniform density. Determine B. the tolerance is +/-2%arrow_forward
- A large wind turbine (typical of the size and specifications of a turbine that you see in a modern wind farm) has three blades connected to a central hub. The blades are 50 m long and rotate at 10 rpm. What angular speed ω and angular acceleration at the tip of a blade?arrow_forwardThe wheel in the figure has eight equally spaced spokes and a radius of 43 cm. It is mounted on a fixed axle and is spinning at 1.1 rev/s. You want to shoot a 25-cm-long arrow parallel to this axle and through the wheel without hitting any of the spokes. Assume that the arrow and the spokes are very thin. What minimum speed must the arrow have? Number i Unitsarrow_forwarda. To lift heavy bricks from the ground to a rooftop, the bricks are placed in a container that is attached to one end of a rope that wraps around a rod coupled to the shaft of a motor. When the motor runs, the buckets will rise. i. Calculate the diameter of the rod so that the bricks can be raised at a constant speed of 3.5 km/h when the motor is running at 490 revolutions per minute? ii. If the bricks are to have an upward acceleration of 0.65 m/s2, calculate the angular acceleration of the rod.arrow_forward
- Solvearrow_forward1. What is the minimum radius Rhump you can use for the semi-circular hump? 2. What is the minimum radius Rloop you can use for the vertical loop?arrow_forwardA. Similar bars as shown are translating and/or rotating with the given linear and angular speeds. Which bar has the greatest amount of kinetic energy? B. Similar bars as shown are translating and/or rotating with the given linear and angular speeds. Which bar has the least amount of kinetic energy?arrow_forward
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