University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Chapter 9, Problem 9.53E
To determine
The moment of inertia of the solid disk.
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Prove that the moment of inertia of a solid sphere of uniform density, when rotating around a diameter,is 2MR2/5, where M is the mass of the sphere and R is the radius.Hint: integrate the infinitesimal volume element in spherical coordinates.
A solid sphere of uniform density has a mass of 2.42 kg and a radius of 0.432 meters. A force of 13.2 Newtons is applied tangentially to the equator of the sphere. If the sphere is free to rotate without friction about an axis perpendicular to the equator to which the 13.2 Newton force is applied, what is the angular acceleration α of the sphere caused by the applied force? It may be useful to bear in mind that the moment of inertia I for a solid sphere of uniform density is I = (2/5)MR^2 where M is the mass of the sphere and R is the radius of the sphere. Also, bear in mind in this case that the torque τ is τ = RF since the force F is applied tangentially to the equator.
A. 15.3 rad/s^2 B. 31.5 rad/s^2 C. 50.3 rad/s^2 D. 68.5 rad/s^2
A uniform solid sphere having mass M = 85.0 g and a radius R = 0.70 m rolls on a horizontal surface and then rolls up an incline at an angle of 60.0º. At the bottom of the incline, the sphere's center of mass has a translational speed of 5.8 m/s. If the frictional losses are negligible, how far does the sphere travel up along the incline?Can you write it out on paper? I'm having a hard time understanding the problem when it is typed out.
Chapter 9 Solutions
University Physics with Modern Physics (14th Edition)
Ch. 9.1 - The figure shows a graph of z and z versus time...Ch. 9.2 - Suppose the disc in Example 9.3 was initially...Ch. 9.3 - Prob. 9.3TYUCh. 9.4 - Suppose the cylinder and block in Example 9.8 have...Ch. 9.5 - A pool cue is a wooden rod of uniform composition...Ch. 9.6 - Two hollow cylinders have the same inner and outer...Ch. 9 - Which of the following formulas is valid if the...Ch. 9 - A diatomic molecule can be modeled as two point...Ch. 9 - What is the difference between tangential and...Ch. 9 - In Fig. Q9.4, all points on the chain have the...
Ch. 9 - In Fig. Q9.4, how are the radial accelerations of...Ch. 9 - A flywheel rotates with constant angular velocity....Ch. 9 - What is the purpose of the spin cycle of a washing...Ch. 9 - You are designing a flywheel to store kinetic...Ch. 9 - Can you think of a body that has the same moment...Ch. 9 - To maximize the moment of inertia of a flywheel...Ch. 9 - How might you determine experimentally the moment...Ch. 9 - A cylindrical body has mass M and radius R. Can...Ch. 9 - Describe how you could use part (b) of Table 9.2...Ch. 9 - A hollow spherical shell of radius R that is...Ch. 9 - For the equations for I given in parts (a) and (b)...Ch. 9 - In part (d) of Table 9.2, the thickness of the...Ch. 9 - Two identical balls, A and B, are each attached to...Ch. 9 - An elaborate pulley consists of four identical...Ch. 9 - You can use any angular measureradians, degrees,...Ch. 9 - When calculating the moment of inertia of an...Ch. 9 - A wheel is rotating about an axis perpendicular to...Ch. 9 - Estimate your own moment of inertia about a...Ch. 9 - (a) What angle in radians is subtended by an are...Ch. 9 - An airplane propeller is rotating at 1900 rpm...Ch. 9 - CP CALC The angular velocity of a flywheel obeys...Ch. 9 - CALC A fan blade rotates with angular velocity...Ch. 9 - CALC A child is pushing a merry-go-round. The...Ch. 9 - CALC At t = 0 the current to a dc electric motor...Ch. 9 - CALC The angle through which a disk drive turns...Ch. 9 - A wheel is rotating about an axis that is in the...Ch. 9 - A bicycle wheel has an initial angular velocity of...Ch. 9 - An electric fan is turned off, and its angular...Ch. 9 - The rotating blade of a blender turns with...Ch. 9 - (a) Derive Eq. (9.12) by combining Eqs. (9.7) and...Ch. 9 - A turntable rotates with a constant 2.25 rad/s2...Ch. 9 - A circular saw blade 0.200 m in diameter starts...Ch. 9 - A high-speed flywheel in a motor is spinning at...Ch. 9 - At t = 0 a grinding wheel has an angular velocity...Ch. 9 - A safety device brings the blade of a power mower...Ch. 9 - In a charming 19th-century hotel, an old-style...Ch. 9 - Using Appendix F, along with the fact that the...Ch. 9 - Compact Disc. A compact disc (CD) stores music in...Ch. 9 - A wheel of diameter 40.0 cm starts from rest and...Ch. 9 - You are to design a rotating cylindrical axle to...Ch. 9 - A flywheel with a radius of 0.300 m starts from...Ch. 9 - An electric turntable 0.750 m in diameter is...Ch. 9 - Centrifuge. An advertisement claims that a...Ch. 9 - At t = 3.00 s a point on the rim of a...Ch. 9 - Electric Drill. According to the shop manual, when...Ch. 9 - Four small spheres, each of which you can regard...Ch. 9 - Calculate the moment of inertia of each of the...Ch. 9 - Calculate the moment of inertia of each of the...Ch. 9 - A uniform bar has two small balls glued to its...Ch. 9 - You are a project manager for a manufacturing...Ch. 9 - A wagon wheel is constructed as shown in Fig....Ch. 9 - An airplane propeller is 2.08 m in length (from...Ch. 9 - A compound disk of outside diameter 140.0 cm is...Ch. 9 - A wheel is turning about an axis through its...Ch. 9 - A uniform sphere with mass 28.0 kg and radius...Ch. 9 - A hollow spherical shell has mass 8.20 kg and...Ch. 9 - The flywheel of a gasoline engine is required to...Ch. 9 - You need to design an industrial turntable that is...Ch. 9 - Energy is to be stored in a 70.0-kg flywheel in...Ch. 9 - A light, flexible rope is wrapped several times...Ch. 9 - A frictionless pulley has the shape of a uniform...Ch. 9 - A bucket of mass m is tied to a massless cable...Ch. 9 - CP A thin, light wire is wrapped around the rim of...Ch. 9 - A uniform 2.00-m ladder of mass 9.00 kg is leaning...Ch. 9 - How I Scales. If we multiply all the design...Ch. 9 - Find the moment of inertia of a hoop (a...Ch. 9 - About what axis will a uniform, balsa-wood sphere...Ch. 9 - (a) For the thin rectangular plate shown in part...Ch. 9 - A thin. rectangular sheet of metal has mass M and...Ch. 9 - A thin uniform rod of mass M and length L is bent...Ch. 9 - Prob. 9.53ECh. 9 - CALC Use Eq. (9.20) to calculate the moment of...Ch. 9 - CALC A slender rod with length L has a mass per...Ch. 9 - CALC A uniform disk with radius R = 0.400 m and...Ch. 9 - CP A circular saw blade with radius 0.120 m starts...Ch. 9 - CALC A roller in a printing press turns through an...Ch. 9 - CP CALC A disk of radius 25.0 cm is free to turn...Ch. 9 - You are designing a rotating metal flywheel that...Ch. 9 - You must design a device for shooting a small...Ch. 9 - Engineers are designing a system by which a...Ch. 9 - A vacuum cleaner bell is looped over a shaft of...Ch. 9 - The motor of a table saw is rotating at 3450...Ch. 9 - While riding a multispeed bicycle, the rider can...Ch. 9 - A computer disk drive is turned on starting from...Ch. 9 - It has been argued that power plants should make...Ch. 9 - A uniform disk has radius R0 and mass M0. Its...Ch. 9 - Measuring I. As an intern at an engineering firm,...Ch. 9 - A uniform, solid disk with mass m and radius R is...Ch. 9 - CP A meter stick with a mass of 0.180 kg is...Ch. 9 - A physics student of mass 43.0 kg is standing at...Ch. 9 - A slender rod is 80.0 cm long and has mass 0.120...Ch. 9 - Exactly one turn of a flexible rope with mass m is...Ch. 9 - The pulley in Fig. P9.75 has radius R and a moment...Ch. 9 - The pulley in Fig. P9.76 has radius 0.160 m and...Ch. 9 - Two metal disks, one with radius R1 = 2.50 cm and...Ch. 9 - A thin, light wire is wrapped around the rim of a...Ch. 9 - In the system shown in Fig. 9.17, a 12.0-kg mass...Ch. 9 - In Fig. P9.80, the cylinder and pulley turn...Ch. 9 - BIO The Kinetic Energy of Walking. If a person of...Ch. 9 - Prob. 9.82PCh. 9 - 810 Human Rotational Energy. A dancer is spinning...Ch. 9 - A thin, uniform rod is bent into a square of side...Ch. 9 - Prob. 9.85PCh. 9 - CALC Neutron Stars and Supernova Remnants. The...Ch. 9 - DATA A technician is testing a...Ch. 9 - DATA You are analyzing the motion of a large...Ch. 9 - DATA You are rebuilding a 1965 Chevrolet. To...Ch. 9 - CALC Calculate the moment of inertia of a uniform...Ch. 9 - CALC On a compact disc (CD), music is coded in a...Ch. 9 - BIO THE SPINNING EEL.American eels (Anguilla...Ch. 9 - BIO THE SPINNING EEL. American eels (Anguilla...Ch. 9 - BIO THE SPINNING EEL.American eels (Anguilla...Ch. 9 - THE SPINNING EEL.American eels (Anguilla rostrata)...
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