Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
4th Edition
ISBN: 9780133942651
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Chapter 12, Problem 76EAP
sThe sphere of mass M and radius R in FIGURE P12.76 is rigidly attached to a thin rod of radius r that passes through the sphere at distance R from the center. A string wrapped around the rod pulls with tension T. Find an expression for the sphere’s
FIGURE P12.76
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Chapter 12 Solutions
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
Ch. 12 - Prob. 1CQCh. 12 - If the angular velocity w is held constant, by...Ch. 12 - FIGURE Q12.3 shows three rotating disks, all of...Ch. 12 - 4. Must an object be rotating to have a moment of...Ch. 12 - 5. The moment of inertia of a uniform rod about an...Ch. 12 - 6. You have two solid steel spheres. Sphere 2 has...Ch. 12 - The professor hands you two spheres. They have the...Ch. 12 - Six forces are applied to the door in FIGURE...Ch. 12 - Prob. 9CQCh. 12 - Rank in order, from largest to smallest, the...
Ch. 12 - The solid cylinder and cylindrical shell in FIGURE...Ch. 12 - A diver in the pike position (legs straight, hands...Ch. 12 - Prob. 13CQCh. 12 - A high-speed drill reaches 2000 rpm in 0.50 s. a....Ch. 12 - A skater holds her arms outstretched as she spins...Ch. 12 - A ceiling fan with 80-cm-diameter blades is...Ch. 12 - An 18-cm-long bicycle crank arm, with a pedal at...Ch. 12 - Prob. 5EAPCh. 12 - The three masses shown in FIGURE EX12.6 are...Ch. 12 - The three masses shown in FIGURE EX12.7 are...Ch. 12 - A 100 g ball and a 200 g ball are connected by a...Ch. 12 - A thin, 100 g disk with a diameter of 8.0 cm...Ch. 12 - What is the rotational kinetic energy of the...Ch. 12 - The three200g masses in FIGURE EX12.11 are...Ch. 12 - A drum major twirls a 96-cm-long, 400 g baton...Ch. 12 - The four masses shown in FIGURE EX12.13 are...Ch. 12 - The four masses shown in FIGURE EXI2.13 are...Ch. 12 - The three masses shown in FIGURE EXI2.15 are...Ch. 12 - A 12-cm-diameter CD has a mass of 21 g. What is...Ch. 12 - A 25 kg solid door is 220 cm tall, 91 cm wide....Ch. 12 - Prob. 18EAPCh. 12 - In FIGURE EX12.19, what magnitude force provides...Ch. 12 - The 20-cm-diameter disk in FIGURE EX12.20 can...Ch. 12 - The axle in FIGURE EXI2.21 is half the distance...Ch. 12 - A 4.0-rn-long, 500 kg steel beam extends...Ch. 12 - An athlete at the gym holds a 3.0 kg steel ball in...Ch. 12 - An object’s moment of inertia is 2.0 kg m2. Its...Ch. 12 - An object whose moment of inertia is 4.0 kg m2...Ch. 12 - A 1.0 kg ball and a 2.0 kg ball are connected by a...Ch. 12 - Starting from rest, a 12-cm-diameter compact disk...Ch. 12 - A 4.0 kg, 36-cm-diameter metal disk, initially at...Ch. 12 - The two objects in FIGURE EXI2.29 are balanced on...Ch. 12 - Prob. 30EAPCh. 12 - The 3.0-rn-long, 100 kg rigid beam of FIGURE...Ch. 12 - A 5.0 kg cat and a 2.0 kg bowl of tuna fish are at...Ch. 12 - A car tire is 60cm in diameter. The car is...Ch. 12 - A 500 g, 8.0-cm-diameter can is filled with...Ch. 12 - Prob. 35EAPCh. 12 - A solid sphere of radius R is placed at a height...Ch. 12 - Prob. 37EAPCh. 12 - Evaluate the cross products AB and CD .Ch. 12 - Prob. 39EAPCh. 12 - Force F=10j N is exerted on a particle at 5i+5j m....Ch. 12 - A 1.3 kg ball on the end of a lightweight rod is...Ch. 12 - What are the magnitude and direction of the...Ch. 12 - What is the angular momentum vector of the 2.0 kg,...Ch. 12 - Prob. 44EAPCh. 12 - Prob. 45EAPCh. 12 - A 2.0 kg, 20-cm-diameter turntable rotates at 100...Ch. 12 - Prob. 47EAPCh. 12 - A toy gyroscope has a ring of mass M and radius R...Ch. 12 - Prob. 49EAPCh. 12 - Prob. 50EAPCh. 12 - Determine the moment of inertia about the axis of...Ch. 12 - What is the moment of inertia of a 2.0 kg,...Ch. 12 - Calculate by direct integration the moment of...Ch. 12 - Calculate the moment of inertia of the rectangular...Ch. 12 - a. A disk of mass M and radius R has a hole of...Ch. 12 - Consider a solid cone of radius R, height H, and...Ch. 12 - Prob. 57EAPCh. 12 - A 3.0-m-long ladder, as shown in Figure 12.35....Ch. 12 - In FIGURE P12.59, an 80 kg construction worker...Ch. 12 - Prob. 60EAPCh. 12 - Prob. 61EAPCh. 12 - A 120-cm-wide sign hangs from a 5.0 kg,...Ch. 12 - Prob. 63EAPCh. 12 - Flywheels are large, massive wheels used to store...Ch. 12 - of mass m1and m2are connected by a massless string...Ch. 12 - The 2.0 kg, 30-cm-diameter disk in FIGURE P12.66...Ch. 12 - A 30-cm-diameter, 1.2 kg solid turntable rotates...Ch. 12 - Your engineering team has been assigned the task...Ch. 12 - A hollow sphere is rolling along a horizontal...Ch. 12 - A 750 g disk and a 760 g ring, both 15 cm in...Ch. 12 - A cylinder of radius R, length L. and mass M is...Ch. 12 - The 5.0 kg, 60-cm-diameter disk in FIGURE P12.72...Ch. 12 - A thin, uniform rod of length L and mass M is...Ch. 12 - A long, thin rod of mass M and length L is...Ch. 12 - The marble rolls down the track shown in FIGURE...Ch. 12 - sThe sphere of mass M and radius R in FIGURE...Ch. 12 - A satellite follows the elliptical orbit shown in...Ch. 12 - A 10 g bullet traveling at 400 m/s strikes a 10...Ch. 12 - A 200 g, 40-cm-diameter turntable rotates on...Ch. 12 - Luc, who is 1.80 m tall and weighs 950 N, is...Ch. 12 - A merry-go-round is a common piece of playground...Ch. 12 - A 45 kg figure skater is spinning on the toes of...Ch. 12 - Prob. 83EAPCh. 12 - The earth’s rotation axis, which is tilted 23.5...Ch. 12 - sThe bunchberry flower has the fastest-moving...Ch. 12 - The two blocks in FIGURE CP12.86 are connected by...Ch. 12 - A rod of length L and mass M has a nonuniform mass...Ch. 12 - In FIGURE CP12.88, a 200 g toy car is placed on a...Ch. 12 - Prob. 89EAPCh. 12 - A 75 g, 30-cm-long rod hangs vertically on a...
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- A 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_forwardA solid sphere of mass m and radius r rolls without slipping along the track shown in Figure P10.83. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. (a) What is the minimum value of h (in terms of R) such that the sphere completes the loop? (b) What are the force components on the sphere at the point P if h = 3R? Figure P10.83arrow_forwardA solid aluminum sphere of radius R has moment of inertia I about an axis through its center. Will the moment of inertia about a central axis of a solid aluminum sphere of radius 2Rbe (a) 2I, (b) 4I, (c) 8I. (d) 16I. or (e) 32I?arrow_forward
- Find 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_forwardThe uniform thin rod in Figure P8.47 has mass M = 3.50 kg and length L = 1.00 m and is free to rotate on a friction less pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of (a) the rods angular acceleration, (b) the tangential acceleration of the rods center of mass, and (c) the tangential acceleration of the rods free end. Figure P8.47 Problems 47 and 86.arrow_forwardThe system shown in Figure P13.18 consisting of four particles connected by massless, rigid rods is rotating around the x axis with an angular speed of 2.50 rad/s. The particle masses are m1 = 1.00 kg, m2 = 4.00 kg, m3 = 2.00 kg, and m4 = 3.00 kg. a. What is the rotational inertia of the system around the x axis? b. Using Kr=12I2 (Eq. 13.10), what is the total rotational kinetic energy of the system? c. What is the tangential speed of each of the four particles? d. Considering the system as four particles in motion and using K=i12mvi2, what is the total kinetic energy of the system? How does this value compare with the result obtained in part (b)? FIGURE P13.18arrow_forward
- 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_forwardAn approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disks center, as in Figure P8.41. The disk has mass 2.50 kg and radius 0.200 m. Each rod has mass 0.850 kg and is 0.750 m long, (a) Find the ceiling fans moment of inertia about a vertical axis through the disks center, (b) Friction exerts a constant torque of magnitude 0.115 N m on the fan as it rotates. Find the magnitude of the constant torque provided by the fans motor if the fan starts from rest and takes 15.0 s and 18.5 full revolutions to reach its maximum speed. Figure P8.41arrow_forwardA long, uniform rod of length L and mass M is pivoted about a frictionless, horizontal pin through one end. The rod is released from rest in a vertical position as shown in Figure P10.65. At the instant the rod is horizontal, find (a) its angular speed, (b) the magnitude of its angular acceleration, (c) the x and y components of the acceleration of its center of mass, and (d) the components of the reaction force at the pivot. Figure P10.65arrow_forward
- Suppose you exert a force of 180 N tangential to a 0.280-m-radius, 75.0-kg grindstone (a solid disk). (a) What torque is exerted? (b) What is the angular acceleration assuming negligible opposing friction? (c) What is the angular acceleration if there is an opposing frictional force of 20.0 N exerted 1.50 cm from the axis?arrow_forwardA bug of mass 0.020 kg is at rest on the edge of a solid cylindrical disk (M=0.10kg,R=0.10m) rotating in a horizontal plane around the vertical axis through its center. The disk is rotating at 10.0 rad/s. The bug crawls to the center of the disk. (a) What is the new angular velocity of the disk? (b) What is the change in the kinetic energy of the system? (c) If the bug crawls back to the outer edge of the disk, what is the angular velocity of the disk then? (d) What is the new kinetic energy of the system? (e) What is the cause of the increase and decrease of kinetic energy?arrow_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_forward
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