
University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)
14th Edition
ISBN: 9780134265414
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Textbook Question
Chapter 10, Problem 10.18DQ
It two spinning objects have the same
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A planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).
Chapter 10 Solutions
University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)
Ch. 10.1 - The accompanying figure shows a force P being...Ch. 10.2 - The figure shows a glider of mass m1 that can...Ch. 10.3 - Suppose the solid cylinder used as a yo-yo in...Ch. 10.4 - You apply equal torques to two different...Ch. 10.5 - A ball is attached to one end of a piece of...Ch. 10.6 - If the polar ice caps were to melt completely due...Ch. 10.7 - Suppose the mass of the flywheel in Fig. 10.34 is...Ch. 10 - Can a single force applied to a body change both...Ch. 10 - Suppose you could use wheels of any type in the...Ch. 10 - Serious bicyclists say that if you reduce the...
Ch. 10 - The harder you hit the brakes while driving...Ch. 10 - When an acrobat walks on a tightrope, she extends...Ch. 10 - When you turn on an electric motor, it takes...Ch. 10 - The work done by a force is the product of force...Ch. 10 - A valued client brings a treasured ball to your...Ch. 10 - You make two versions of the same object out of...Ch. 10 - Two identical masses are attached to frictionless...Ch. 10 - The force of gravity acts on the baton in Fig....Ch. 10 - A certain solid uniform bail reaches a maximum...Ch. 10 - A wheel is rolling without slipping on a...Ch. 10 - A hoop, a uniform solid cylinder, a spherical...Ch. 10 - A ball is rolling along al speed without slipping...Ch. 10 - You are standing at the center of a large...Ch. 10 - Global Warming. If the earths climate continues to...Ch. 10 - It two spinning objects have the same angular...Ch. 10 - A student is sitting on a frictionless rotating...Ch. 10 - A point particle travels in a straight line at...Ch. 10 - In Example 10.10 (Section 10.6) the angular speed ...Ch. 10 - In Example 10.10 (Section 10.6) the rotational...Ch. 10 - As discussed in Section 10.6, the angular momentum...Ch. 10 - If you stop a spinning raw egg for the shortest...Ch. 10 - A helicopter has a large main rotor that rotates...Ch. 10 - In a common design for a gyroscope, the flywheel...Ch. 10 - A gyroscope is precessing about a vertical axis....Ch. 10 - A gyroscope takes 3.8 s to precess 1.0 revolution...Ch. 10 - A gyroscope is precessing as in Fig. 10.32. What...Ch. 10 - A bullet spins on its axis as it emerges from a...Ch. 10 - Calculate the torque (magnitude and direction)...Ch. 10 - Calculate the net torque about point O for the two...Ch. 10 - A square metal plate 0.180m on each side is...Ch. 10 - Three forces are applied to a wheel of radius...Ch. 10 - One force acting on a machine part is...Ch. 10 - A metal bar is in the xy-plane with one end of the...Ch. 10 - A machinist is using a wrench lo loosen a nut. The...Ch. 10 - A uniform disk with mass 40.0 kg and radius 0.200...Ch. 10 - The flywheel of an engine has moment of inertia...Ch. 10 - A cord is wrapped around ihe rim of a solid...Ch. 10 - A machine part has the shape of u solid uniform...Ch. 10 - CP A stone is suspended from the free end of a...Ch. 10 - Prob. 10.13ECh. 10 - CP A 15.0-kg bucket of water is suspended by a...Ch. 10 - A wheel rotates without friction about a...Ch. 10 - A 12.0-kg box resting on a horizontal,...Ch. 10 - A 2.20-kg hoop 1.20 m in diameter is rolling to...Ch. 10 - BIO Gymnastics. We can roughly model a gymnastic...Ch. 10 - What fraction of the total kinetic energy is...Ch. 10 - A siring is wrapped several times around the rim...Ch. 10 - A solid ball is released from rest and slides down...Ch. 10 - A hollow, spherical shell with mass 2.00 kg rolls...Ch. 10 - A 392-N wheel comes off a moving truck and rolls...Ch. 10 - A uniform marble rolls down a symmetrical bowl,...Ch. 10 - A thin, light string is wrapped around the outer...Ch. 10 - A Ball Rolling Uphill. A bowling ball rolls...Ch. 10 - A size-5 soccer ball of diameter 22.6 cm and mass...Ch. 10 - A size-5 soccer ball of diameter 22.6 cm and mass...Ch. 10 - A playground merry-go-round has radius 2.40 m and...Ch. 10 - An engine delivers 175 hp to an aircraft propeller...Ch. 10 - A 2.80-kg grinding wheel is in the form of a solid...Ch. 10 - An electric motor consumes 9.00 kJ of electrical...Ch. 10 - (a) Compute the torque developed by an industrial...Ch. 10 - An airplane propeller is 2.08 m in length (from...Ch. 10 - A 2.00-kg rock has a horizontal velocity of...Ch. 10 - A woman with mass 50 kg is standing on the rim of...Ch. 10 - Find the magnitude of the angular momentum of the...Ch. 10 - (a) Calculate the magnitude of the angular...Ch. 10 - CALC A hollow, thin-walled sphere of mass 12.0 kg...Ch. 10 - CP A small block on a frictionless, horizontal...Ch. 10 - Prob. 10.41ECh. 10 - A diver comes off a board with arms straight up...Ch. 10 - The Spinning Figure Skater. The outstretched hands...Ch. 10 - A solid wood door 1.00 m wide and 2.00 m high is...Ch. 10 - A large wooden turntable in the shape of a flat...Ch. 10 - Asteroid Collision! Suppose that an asteroid...Ch. 10 - Prob. 10.47ECh. 10 - A thin uniform rod has a length of 0.500 m and is...Ch. 10 - A thin, uniform metal bar. 2.00 m long and...Ch. 10 - A uniform. 4.5-kg, square, solid wooden gate 1.5 m...Ch. 10 - The rotor (flywheel) of a loy gyroscope has mass...Ch. 10 - A Gyroscope on the Moon. A certain gyroscope...Ch. 10 - Stabilization of the Hubble Space Telescope. The...Ch. 10 - A 50.0-kg grindstone is a solid disk 0.520 m in...Ch. 10 - 10.55A grindstone in the shape of a solid disk...Ch. 10 - A uniform, 8.40-kg, spherical shell 50.0 cm in...Ch. 10 - A thin, uniform. 3.80-kg bar, 80.0 cm long, has...Ch. 10 - You are designing a simple elevator system for an...Ch. 10 - The Atwoods Machine. Figure P10.59 illustrates an...Ch. 10 - The mechanism shown in Fig. P10.60 is used to...Ch. 10 - A large 16.0-kg roll of paper with radius R = 18.0...Ch. 10 - A block with mass m = 5.00 kg slides down a...Ch. 10 - Two metal disks, one with radius R1 = 2.50 cm and...Ch. 10 - A lawn roller in the form of a thin-walled, hollow...Ch. 10 - Two weights are connected by a very light,...Ch. 10 - You complain about fire safety to the landlord of...Ch. 10 - The Yo-yo. A yo-yo is made from two uniform disks,...Ch. 10 - CP A thin-walled, hollow spherical shell of mass m...Ch. 10 - A basketball (which can be closely modeled as a...Ch. 10 - CP A solid uniform ball rolls without slipping up...Ch. 10 - Rolling Stones. A solid, uniform, spherical...Ch. 10 - You are designing a system for moving aluminum...Ch. 10 - A 42.0-cm-diameter wheel, consisting of a rim and...Ch. 10 - A uniform, 0.0300-kg rod of length 0.400 in...Ch. 10 - A uniform solid cylinder with mass M and radius 2R...Ch. 10 - Tarzan and Jane in the 21st Century. Tarzan has...Ch. 10 - A 5.00-kg ball is dropped from a height of 12.0 m...Ch. 10 - The solid wood door of a gymnasium is 1.00 m wide...Ch. 10 - A uniform rod of length L rests on a friction less...Ch. 10 - CP A large turntable with radius 6.00 m rotates...Ch. 10 - In your job as a mechanical engineer you are...Ch. 10 - A local ice hockey team has asked you to design an...Ch. 10 - You are designing a slide for a water park. In a...Ch. 10 - Neutron Star Glitches. Occasionally, a rotating...Ch. 10 - A 500.0-g bird is flying horizontally at 2.25 m/s,...Ch. 10 - CP A small block with mass 0.130 kg is attached to...Ch. 10 - A 55-kg runner runs around the edge of a...Ch. 10 - DATA The V6 engine in a 2014 Chevrolet Silverado...Ch. 10 - DATA You have one object of each of these shapes,...Ch. 10 - DATA You are testing a small flywheel (radius...Ch. 10 - CALC A block with mass m is revolving with linear...Ch. 10 - When an object is rolling without slipping, the...Ch. 10 - A demonstration gyroscope wheel is constructed by...Ch. 10 - The moment of inertia of the empty turntable is...Ch. 10 - While the turntable is being accelerated, the...Ch. 10 - A doubling of the torque produces a greater...Ch. 10 - If the bodys center of mass were not placed on the...
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