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A plank with a mass M = 6.00 kg rests on top of two identical, solid, cylindrical rollers that have R = 5.00 cm and m = 2.00 kg (Fig. P10.87). The plank is pulled by a constant horizontal force
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- A uniform solid sphere of mass m and radius r is releasedfrom rest and rolls without slipping on a semicircular ramp ofradius R r (Fig. P13.76). Ifthe initial position of the sphereis at an angle to the vertical,what is its speed at the bottomof the ramp? FIGURE P13.76arrow_forwardA square plate with sides 2.0 m in length can rotatearound an axle passingthrough its center of mass(CM) and perpendicular toits surface (Fig. P12.53). There are four forces acting on the plate at differentpoints. The rotational inertia of the plate is 24 kg m2. Use the values given in the figure to answer the following questions. a. Whatis the net torque acting onthe plate? b. What is theangular acceleration of the plate? FIGURE P12.53 Problems 53 and 54.arrow_forwardReview. An object with a mass of m = 5.10 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.250 m and mass M = 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center as shown in Figure P10.45. The suspended object is released from rest 6.00 m above the floor. Determine (a) the tension in the string, (b) the acceleration of the object, and (c) the speed with which the object hits the floor. (d) Verify your answer to part (c) by using the isolated system (energy) model. Figure P10.45arrow_forward
- Consider the disk in Problem 71. The disks outer rim hasradius R = 4.20 m, and F1 = 10.5 N. Find the magnitude ofeach torque exerted around the center of the disk. FIGURE P12.71 Problems 71-75arrow_forwardA tennis ball is a hollow sphere with a thin wall. It is set rolling without slipping at 4.03 m/s on a horizontal section of a track as shown in Figure P10.62. It rolls around the inside of a vertical circular loop of radius r = 45.0 cm. As the ball nears the bottom of the loop, the shape of the track deviates from a perfect circle so that the ball leaves the track at a point h = 20.0 cm below the horizontal section. (a) Find the balls speed at the top of the loop. (b) Demonstrate that the ball will not fall from the track at the top of the loop. (c) Find the balls speed as it leaves the track at the bottom. What If? (d) Suppose that static friction between ball and track were negligible so that the ball slid instead of rolling. Would its speed then be higher, lower, or the same at the top of the loop? (e) Explain your answer to part (d). Figure P10.62arrow_forwardFigure P10.16 shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter. Calculate (a) the speed of a link of the chain relative to the bicycle frame, (b) the angular speed of the bicycle wheels, and (c) the speed of the bicycle relative to the road. (d) What pieces of data, if any, are not necessary for the calculations? Figure P10.16arrow_forward
- Review. An object with a mass of m = 5.10 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.250 m and mass M = 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center as shown in Figure P10.29. The suspended object is released from rest 6.00 m above the floor. Determine (a) the tension in the string, (b) the acceleration of the object, and (c) the speed with which the object hits the floor. (d) Verify your answer to part (c) by using the isolated system (energy) model. Figure P10.29arrow_forwardThe angular momentum vector of a precessing gyroscope sweeps out a cone as shown in Figure P11.31. The angular speed of the tip of the angular momentum vector, called its precessional frequency, is given by p=/I, where is the magnitude of the torque on the gyroscope and L is the magnitude of its angular momentum. In the motion called precession of the equinoxes, the Earths axis of rotation processes about the perpendicular to its orbital plane with a period of 2.58 104 yr. Model the Earth as a uniform sphere and calculate the torque on the Earth that is causing this precession. Figure P11.31 A precessing angular momentum vector sweeps out a cone in space.arrow_forwardFind the net torque on the wheel in Figure P10.23 about the axle through O, taking a = 10.0 cm and b = 25.0 cm. Figure P10.23arrow_forward
- A ball of mass M = 5.00 kg and radius r = 5.00 cm isattached to one end of a thin,cylindrical rod of length L = 15.0 cm and mass m = 0.600 kg.The ball and rod, initially at restin a vertical position and freeto rotate around the axis shownin Figure P13.70, are nudgedinto motion. a. What is therotational kinetic energy of thesystem when the ball and rodreach a horizontal position? b. What is the angular speed of the ball and rod when they reach a horizontal position? c. What is the linear speed of the centerof mass of the ball when the ball and rod reach a horizontalposition? d. What is the ratio of the speed found in part (c) tothe speed of a ball that falls freely through the same distance? FIGURE P13.70arrow_forwardA disk with a radius of 4.5 m has a 100-N force applied to its outer edge at two different angles (Fig. P12.55). The disk has arotational inertia of 165 kg m2. a. What is the magnitude of the torque applied to the disk incase 1? b. What is the magnitude of the torque applied to the disk incase 2? c. Assuming the force on the disk is constant in each case,what is the magnitude of the angular acceleration applied tothe disk in each case? d. Which case is a more effective way of spinning the disk?Describe which quantity you are using to determine effectiveness and why you chose that quantity. FIGURE P12.55arrow_forwardReview. A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of = 30.0 as shown in Figure P10.16. The coefficient of kinetic friction is 0.360 for both blocks. (a) Draw force diagrams of both blocks and of the pulley. Determine (b) the acceleration of the two blocks and (c) the tensions in the string on both sides of the pulley. Figure P10.16arrow_forward
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