Concept explainers
* Superball If you give a superball backspin and throw it toward a horizontal floor, it is possible that the ball bounces backward, as shown in Figure P9.71. If the ball has a color pattern or stripes, you may also notice that during the collision with the ground, the direction of rotation of the ball changes, as indicated in the figure. Both changes (the change of the ball’s translational velocity and the change of the balls
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- Additional Problems A typical propeller of a turbine used to generate electricity from the wind consists of three blades as in Figure P8.75. Each blade has a length of L = 35 in and a mass of m = 420 kg. The propeller rotates at the rate of 25 rev/min. (a) Convert the angular speed of the propeller to units of rad/s. Find (b) the moment of inertia of the propeller about the axis of rotation and (c) the total kinetic, energy of the propeller. Figure P8.75arrow_forwardA light rod of length 2L is free to rotate in a vertical plane about a frictionless pivot through its center. A particle of mass m1 is attached at one end of the rod, and a mass m2 is at the opposite end, where m1 m2. The system is released from rest in the vertical position shown in Figure P8.84a, and at some later time, the system is rotating in the Position shown in Figure P8.84b. Take the reference point of the gravitational potential energy to be at the pivot, (a) Find an expression for the system's total mechanical energy in the vertical position. (b) Find an expression for the total mechanical energy in the rotated position shown in Figure P8.84b. (c) Using the fact that the mechanical energy of the system is conserved, how would you determine the angular speed co of the system in the rotated position? (d) Find the magnitude of the torque on the system in the vertical position and in the routed position. Is the torque constant? Explain what these results imply regarding the angular momentum of the system, (c) Find an expression for the magnitude of the angular acceleration of the system in the rotated position. Does your result make sense when the rod is horizontal? When it is vertical? Explain. Figure P8.84arrow_forwardA ball having mass m is fastened at the end of a flagpole that is connected to the side of a tall building at point P as shown in Figure P11.15. The length of the flagpole is , and it makes an angle with the x axis. The ball becomes loose and starts to fall with acceleration gj. (a) Determine the angular momentum of the ball about point P as a function of time. (b) For what physical reason does the angular momentum change? (c) What is the rate of change of the angular momentum of the ball about point P? Figure P11.15arrow_forward
- A cat usually lands on its feet regardless of the position from which it is dropped. A slow-motion film of a cat falling shows that the upper half of its body twists in one direction while the lower half twists in the opposite direction. (See Fig. CQ8.14.) Why does this type of rotation occur? Figure CQ8.14arrow_forwardAs shown in Figure OQ10.7, a cord is wrapped onto a cylindrical reel mounted on a fixed, friction less, horizontal axle. When does the reel have a greater magnitude of angular acceleration? (a) When the cord is pulled down with a constant force of 50 N. (b) When an object of weight 50 X is hung from the cord and released, (c) The angular accelerations in parts (a) and (b) are equal, (d) It is impossible to determine.arrow_forwardFour objects are held in position at the corners of a rectangle by light rods as shown in Figure P8.37. Find the moment of inertia of the system about (a) the x-axis, (b) they-axis, and (c) an axis through O and perpendicular to the page.arrow_forward
- Unreasonable 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(a) Calculate the angular momentum of the Earth in its orbit around the Sun. (b) Compare this angular momentum with the angular momentum of Earth on its axis.arrow_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
- 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_forwardA cat usually lands on its feet regardless of the position from which it is dropped. A slow-motion film of a cat falling shows that the upper half of its body twists in one direction while the lower half twists in the opposite direction. (See Fig. CQ8.14.) Why does this type of rotation occur? Figure CQ8.14arrow_forwardWhile punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.75kgm2 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?arrow_forward
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