Problem Q9.1DQ: Which of the following formulas is valid if the angular acceleration of an object is not constant?... Problem Q9.2DQ: A diatomic molecule can be modeled as two point masses, m1 and m2, slightly separated (Fig. Q9.2).... Problem Q9.3DQ: What is the difference between tangential and radial acceleration for a point on a rotating body? Problem Q9.4DQ: In Fig. Q9.4, all points on the chain have the same linear speed. Is the magnitude of the linear... Problem Q9.5DQ: In Fig. Q9.4, how are the radial accelerations of points at the teeth of the two sprockets related?... Problem Q9.6DQ: A flywheel rotates with constant angular velocity. Does a point on its rim have a tangential... Problem Q9.7DQ: What is the purpose of the spin cycle of a washing machine? Explain in terms of acceleration... Problem Q9.8DQ: You are designing a flywheel to store kinetic energy. If all of the following uniform objects have... Problem Q9.9DQ: Can you think of a body that has the same moment of inertia for all possible axes? If so, give an... Problem Q9.10DQ: To maximize the moment of inertia of a flywheel while minimizing its weight, what shape and... Problem Q9.11DQ: How might you determine experimentally the moment of inertia of an irregularly shaped body about a... Problem Q9.12DQ: A cylindrical body has mass M and radius R. Can the mass be distributed within the body in such a... Problem Q9.13DQ: Describe how you could use part (b) of Table 9.2 to derive the result in part (d). Problem Q9.14DQ: A hollow spherical shell of radius R that is rotating about an axis through its center has... Problem Q9.15DQ: For the equations for I given in parts (a) and (b) of Table 9.2 to be valid, must the rod have a... Problem Q9.16DQ: In part (d) of Table 9.2, the thickness of the plate must be much less than a for the expression... Problem Q9.17DQ: Two identical balls, A and B, are each attached to very light string, and each string is wrapped... Problem Q9.18DQ: An elaborate pulley consists of four identical balls at the ends of spokes extending out from a... Problem Q9.19DQ: You can use any angular measureradians, degrees, or revolutionsin some of the equations in Chapter... Problem Q9.20DQ: When calculating the moment of inertia of an object, can we treat all its mass as if it were... Problem Q9.21DQ: A wheel is rotating about an axis perpendicular to the plane of the wheel and passing through the... Problem Q9.22DQ: Estimate your own moment of inertia about a vertical axis through the center of the top of your head... Problem Q9.1E: (a) What angle in radians is subtended by an are 1.50 m long on the circumference of a circle of... Problem 9.2E: An airplane propeller is rotating at 1900 rpm (rev/min). (a) Compute the propellers angular velocity... Problem 9.3E: CP CALC The angular velocity of a flywheel obeys the equation z (t) = A + Bt2, where t is in seconds... Problem 9.4E: CALC A fan blade rotates with angular velocity given by z(t) = t2, where = 5.00 rad/s and =... Problem 9.5E: CALC A child is pushing a merry-go-round. The angle through which the merry-go-round has turned... Problem 9.6E: CALC At t = 0 the current to a dc electric motor is reversed, resulting in an angular displacement... Problem 9.7E: CALC The angle through which a disk drive turns is given by (t) = a + bt ct3, where a, b, and c... Problem 9.8E: A wheel is rotating about an axis that is in the z-direction. The angular velocity z. is 6.00 rad/s... Problem 9.9E: A bicycle wheel has an initial angular velocity of 1.50 rad/s. (a) If its angular acceleration is... Problem 9.10E: An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200... Problem 9.11E: The rotating blade of a blender turns with constant angular acceleration l.50 rad/s2. (a) How much... Problem 9.12E: (a) Derive Eq. (9.12) by combining Eqs. (9.7) and (9.11) to eliminate t. (b) The angular velocity of... Problem 9.13E: A turntable rotates with a constant 2.25 rad/s2 angular acceleration. After 4.00 s it has rotated... Problem 9.14E: A circular saw blade 0.200 m in diameter starts from rest. In 6.00 s it accelerates with constant... Problem 9.15E: A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The... Problem 9.16E: At t = 0 a grinding wheel has an angular velocity of 24.0 rad/s. It has a constant angular... Problem 9.17E: A safety device brings the blade of a power mower from an initial angular speed of 1 to rest in 1.00... Problem 9.18E: In a charming 19th-century hotel, an old-style elevator is connected to a counterweight by a cable... Problem 9.19E: Using Appendix F, along with the fact that the earth spins on its axis once per day, calculate (a)... Problem 9.20E: Compact Disc. A compact disc (CD) stores music in a coded pattern of tiny pits 107 m deep. The pits... Problem 9.21E: A wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of... Problem 9.22E: You are to design a rotating cylindrical axle to lift 800-N buckets of cement from the ground to a... Problem 9.23E: A flywheel with a radius of 0.300 m starts from rest and accelerates with a constant angular... Problem 9.24E: An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular... Problem 9.25E: Centrifuge. An advertisement claims that a centrifuge takes up only 0.127 m of bench space but can... Problem 9.26E: At t = 3.00 s a point on the rim of a 0.200-m-radius wheel has a tangential speed of 50.0 m/s as the... Problem 9.27E: Electric Drill. According to the shop manual, when drilling a 12.7-mm-diameter hole in wood,... Problem 9.28E: Four small spheres, each of which you can regard as a point of mass 0.200 kg, are arranged in a... Problem 9.29E: Calculate the moment of inertia of each of the following uniform objects about the axes indicated.... Problem 9.30E: Calculate the moment of inertia of each of the following uniform objects about the axes indicated.... Problem 9.31E: A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and has mass 4.00 kg,... Problem 9.32E: You are a project manager for a manufacturing company. One of the machine parts on the assembly line... Problem 9.33E: A wagon wheel is constructed as shown in Fig. E9.33. The radius of the wheel is 0.300 m, and the rim... Problem 9.34E: An airplane propeller is 2.08 m in length (from tip to tip) with mass 117 kg and is rotating at 2400... Problem 9.35E: A compound disk of outside diameter 140.0 cm is made up of a uniform solid disk of radius 50.0 cm... Problem 9.36E: A wheel is turning about an axis through its center with constant angular acceleration. Starting... Problem 9.37E: A uniform sphere with mass 28.0 kg and radius 0.380 m is rotating at constant angular velocity about... Problem 9.38E: A hollow spherical shell has mass 8.20 kg and radius 0.220 m. It is initially at rest and then... Problem 9.39E: The flywheel of a gasoline engine is required to give up 500 J of kinetic energy while its angular... Problem 9.40E: You need to design an industrial turntable that is 60.0 cm in diameter and has a kinetic energy of... Problem 9.41E: Energy is to be stored in a 70.0-kg flywheel in the shape of a uniform solid disk with radius R =... Problem 9.42E: A light, flexible rope is wrapped several times around a hollow cylinder, with a weight of 40.0 N... Problem 9.43E: A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius 20.0 cm. A... Problem 9.44E: A bucket of mass m is tied to a massless cable that is wrapped around the outer rim of a... Problem 9.45E: CP A thin, light wire is wrapped around the rim of a wheel (Fig. E9.45). The wheel rotates without... Problem 9.46E: A uniform 2.00-m ladder of mass 9.00 kg is leaning against a vertical wall while making an angle of... Problem 9.47E: How I Scales. If we multiply all the design dimensions of an object by a scaling factor f, its... Problem 9.48E: Find the moment of inertia of a hoop (a thin-walled, hollow ring) with mass M and radius R about an... Problem 9.49E: About what axis will a uniform, balsa-wood sphere have the same moment of inertia as does a... Problem 9.50E: (a) For the thin rectangular plate shown in part (d) of Table 9.2, find the moment of inertia about... Problem 9.51E: A thin. rectangular sheet of metal has mass M and sides of length a and b. Use the parallel-axis... Problem 9.52E: A thin uniform rod of mass M and length L is bent at its center so that the two segments are now... Problem 9.53E: CALC Use Eq. (9.20) to calculate the moment of inertia of a uniform, solid disk with mass M and... Problem 9.54E: CALC Use Eq. (9.20) to calculate the moment of inertia of a slender, uniform rod with mass M and... Problem 9.55E: CALC A slender rod with length L has a mass per unit length that varies with distance from the left... Problem 9.56P: CALC A uniform disk with radius R = 0.400 m and mass 30.0 kg rotates in a horizontal plane on a... Problem 9.57P: CP A circular saw blade with radius 0.120 m starts from rest and turns in a vertical plane with a... Problem 9.58P: CALC A roller in a printing press turns through an angle (t) given by (t) = t2 t3, where = 3.20... Problem 9.59P: CP CALC A disk of radius 25.0 cm is free to turn about an axle perpendicular to it through its... Problem 9.60P: You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to be... Problem 9.61P: You must design a device for shooting a small marble vertically upward. The marble is in a small cup... Problem 9.62P: Engineers are designing a system by which a falling mass m imparts kinetic energy to a rotating... Problem 9.63P: A vacuum cleaner bell is looped over a shaft of radius 0.45 cm and a wheel of radius 1.80 cm. The... Problem 9.64P: The motor of a table saw is rotating at 3450 rev/min. A pulley attached to the motor shaft drives a... Problem 9.65P: While riding a multispeed bicycle, the rider can select the radius of the rear sprocket that is... Problem 9.66P: A computer disk drive is turned on starting from rest and has constant angular acceleration. If it... Problem 9.67P: It has been argued that power plants should make use of off-peak hours (such as late at night) to... Problem 9.68P: A uniform disk has radius R0 and mass M0. Its moment of inertia for an axis perpendicular to the... Problem 9.69P: Measuring I. As an intern at an engineering firm, you are asked to measure the moment of inertia of... Problem 9.70P: A uniform, solid disk with mass m and radius R is pivoted about a horizontal axis through its... Problem 9.71P: CP A meter stick with a mass of 0.180 kg is pivoted about one end so it can rotate without friction... Problem 9.72P: A physics student of mass 43.0 kg is standing at the edge of the flat roof of a building, 12.0 m... Problem 9.73P: A slender rod is 80.0 cm long and has mass 0.120 kg. A small 0.0200-kg sphere is welded to one end... Problem 9.74P: Exactly one turn of a flexible rope with mass m is wrapped around a uniform cylinder with mass M and... Problem 9.75P: The pulley in Fig. P9.75 has radius R and a moment of inertia I. The rope does not slip over the... Problem 9.76P: The pulley in Fig. P9.76 has radius 0.160 m and moment of inertia 0.380 kg m2. The rope does not... Problem 9.77P: Two metal disks, one with radius R1 = 2.50 cm and mass M1 = 0.80 kg and the other with radius R2 =... Problem 9.78P: A thin, light wire is wrapped around the rim of a wheel as shown in Fig. E9.45. The wheel rotates... Problem 9.79P: In the system shown in Fig. 9.17, a 12.0-kg mass is released from rest and falls, causing the... Problem 9.80P: In Fig. P9.80, the cylinder and pulley turn without friction about stationary horizontal axles that... Problem 9.81P: BIO The Kinetic Energy of Walking. If a person of mass M simply moved forward with speed V, his... Problem 9.82P: BIO The Kinetic Energy of Running. Using Problem 9.81 as a guide, apply it to a person running at 12... Problem 9.83P: 810 Human Rotational Energy. A dancer is spinning at 72 rpm about an axis through her center with... Problem 9.84P: A thin, uniform rod is bent into a square of side length a. If the total mass is M, find the moment... Problem 9.85P: CALC A sphere with radius R = 0.200 m has density that decreases with distance r from the center of... Problem 9.86P: CALC Neutron Stars and Supernova Remnants. The Crab Nebula is a cloud of glowing gas about 10... Problem 9.87P: DATA A technician is testing a computer-controlled, variable-speed motor. She attaches a thin disk... Problem 9.88P: DATA You are analyzing the motion of a large flywheel that has radius 0.800 m. In one test run, the... Problem 9.89P: DATA You are rebuilding a 1965 Chevrolet. To decide whether to replace the flywheel with a newer,... Problem 9.90CP: CALC Calculate the moment of inertia of a uniform solid cone about an axis through its center (Fig.... Problem 9.91CP: CALC On a compact disc (CD), music is coded in a pattern of tins pits arranged in a track that... Problem 9.92PP: BIO THE SPINNING EEL.American eels (Anguilla rostrata) are freshwater fish with long, slender bodies... Problem 9.93PP: BIO THE SPINNING EEL. American eels (Anguilla rostrata) are freshwater fish with long, slender... Problem 9.94PP: BIO THE SPINNING EEL.American eels (Anguilla rostrata) are freshwater fish with long, slender bodies... Problem 9.95PP: THE SPINNING EEL.American eels (Anguilla rostrata) are freshwater fish with long, slender bodies... format_list_bulleted