Physics for Scientists and Engineers with Modern Physics

4th Edition

ISBN: 9780131495081

Author: Douglas C. Giancoli

Publisher: Addison-Wesley

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Chapter 10, Problem 22P

(II) The angle through which a rotating wheel has turned in time t is given by θ = 8.5 t − 15.0 t 2 + 1.6 t 4 , where θ is in radians and t in seconds. Determine an expression (a) for the instantaneous angular velocity ω and (b) for the instantaneous angular acceleration α. (c) Evaluate ω and α at t = 3.0 s. (d) What is the average angular velocity, and (e) the average angular acceleration between t = 2.0s and t = 3.0 s?

Definition Definition Angle at which a point rotates around a specific axis or center in a given direction. Angular displacement is a vector quantity and has both magnitude and direction. The angle built by an object from its rest point to endpoint created by rotational motion is known as angular displacement. Angular displacement is denoted by θ, and the S.I. unit of angular displacement is radian or rad.

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Chapter 10, Problem 21P

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Chapter 10 Solutions

Physics for Scientists and Engineers with Modern Physics

Ch. 10.1 - In Example 103, we found that the carousel, after...Ch. 10.4 - Two forces (FB = 20 N and FA = 30 N) are applied...Ch. 10.7 - In Figs. 1020f and g, the moments of inertia for a...Ch. 10.8 - Estimate the energy stored in the rotational...Ch. 10.9 - Return to the Chapter-Opening Question, p. 248,...Ch. 10.9 - Find the acceleration a of a yo-yo whose spindle...Ch. 10 - A bicycle odometer (which counts revolutions and...Ch. 10 - Suppose a disk rotates at constant angular...Ch. 10 - Could a nonrigid object be described by a single...Ch. 10 - Can a small force ever exert a greater torque than...

Ch. 10 - Why is it more difficult to do a sit-up with your...Ch. 10 - Mammals that depend on being able to run fast have...Ch. 10 - If the net force on a system is zero, is the net...Ch. 10 - Two inclines have the same height but make...Ch. 10 - Two spheres look identical and have the same mass....Ch. 10 - Two solid spheres simultaneously start rolling...Ch. 10 - Why do tightrope walkers (Fig. 1043) carry a long,...Ch. 10 - A sphere and a cylinder have the same radius and...Ch. 10 - The moment of inertia of this textbook would be...Ch. 10 - The moment of inertia of a rotating solid disk...Ch. 10 - Prob. 15Q Ch. 10 - (I) Express the following angles in radians: (a)...Ch. 10 - Prob. 2P Ch. 10 - Prob. 3P Ch. 10 - (I) The blades in a blender rotate at a rate of...Ch. 10 - (II) (a) A grinding wheel 0.35 m in diameter...Ch. 10 - (II) A bicycle with tires 68 cm in diameter...Ch. 10 - (II) Calculate the angular velocity of (a) the...Ch. 10 - (II) A rotating merry-go-round makes one complete...Ch. 10 - (II) What is the linear speed of a point (a) on...Ch. 10 - (II) Calculate the angular velocity of the Earth...Ch. 10 - Prob. 11P Ch. 10 - (II) A 64-cm-diameter wheel accelerates uniformly...Ch. 10 - (II) In traveling to the Moon, astronauts aboard...Ch. 10 - (II) A turntable of radius R1 is turned by a...Ch. 10 - (II) The axle of a wheel is mounted on supports...Ch. 10 - (I) An automobile engine slows down from 3500 rpm...Ch. 10 - (I) A centrifuge accelerates uniformly front rest...Ch. 10 - (I) Pilots can be tested for the stresses of...Ch. 10 - (II) A cooling fan is turned off when it is...Ch. 10 - (II) Using calculus, derive the angular kinematic...Ch. 10 - (II) A small rubber wheel is used to drive a large...Ch. 10 - (II) The angle through which a rotating wheel has...Ch. 10 - (II) The angular acceleration of a wheel, as a...Ch. 10 - (I) A 62-kg person riding a bike puts all her...Ch. 10 - (I) Calculate the net torque about the axle of the...Ch. 10 - (II) A person exerts a horizontal force of 32 N on...Ch. 10 - (II) Two blocks, each of mass m, are attached to...Ch. 10 - (II) A wheel of diameter 27.0 cm is constrained to...Ch. 10 - (II) The bolts on the cylinder head of an engine...Ch. 10 - (II) Determine the net torque on the 2.0-m-long...Ch. 10 - (I) Determine the moment of inertia of a 10.8-kg...Ch. 10 - (I) Estimate the moment of inertia of a bicycle...Ch. 10 - (II) A potter is shaping a bowl on a potters wheel...Ch. 10 - (II) An oxygen molecule consists of two oxygen...Ch. 10 - (II) A softball player swings a bat, accelerating...Ch. 10 - (II) A grinding wheel is a uniform cylinder with a...Ch. 10 - (II) A small 650-g ball on the end of a thin,...Ch. 10 - (II) The forearm in Fig. 1052 accelerates a 3.6-kg...Ch. 10 - (II) Assume that a 1.00-kg ball is thrown solely...Ch. 10 - (II) Calculate the moment of inertia of the array...Ch. 10 - (II) A merry-go-round accelerates from rest to...Ch. 10 - (II) A 0.72-m-diameter solid sphere can be rotated...Ch. 10 - (II) Suppose the force FT in the cord hanging from...Ch. 10 - (II) A dad pushes tangentially on a small...Ch. 10 - Prob. 45P Ch. 10 - (II) Two blocks are connected by a light string...Ch. 10 - (II) A helicopter rotor blade can be considered a...Ch. 10 - (II) A centrifuge rotor rotating at 10,300 rpm is...Ch. 10 - (II) When discussing moments of inertia,...Ch. 10 - Prob. 50P Ch. 10 - (III) An Atwoods machine consists of two masses,...Ch. 10 - (III) A string passing over a pulley has a 3.80-kg...Ch. 10 - (III) A hammer thrower accelerates the hammer...Ch. 10 - (III) A thin rod of length l stands vertically on...Ch. 10 - (I) Use the parallel-axis theorem to show that the...Ch. 10 - (II) Determine the moment of inertia of a 19-kg...Ch. 10 - (II) Two uniform solid spheres of mass M and...Ch. 10 - (II) A ball of mass M and radius r1 on the end of...Ch. 10 - (II) A thin 7.0-kg wheel of radius 32 cm is...Ch. 10 - (III) Derive the formula for the moment of inertia...Ch. 10 - (III) (a) Derive the formula given in Fig. 1020h...Ch. 10 - (I) An automobile engine develops a torque of 255m...Ch. 10 - (I) A centrifuge rotor has a moment of inertia of...Ch. 10 - (II) A rotating uniform cylindrical platform of...Ch. 10 - (II) A merry-go-round has a mass of 1640 kg and a...Ch. 10 - (II) A Uniform thin rod of length l and mass M is...Ch. 10 - (II) Two masses, mA = 35.0 kg and mB = 38.0 kg,...Ch. 10 - (III) A 4.00-kg mass and a 3.00-kg mass are...Ch. 10 - (III) A 2.30-m-long pole is balanced vertically on...Ch. 10 - (I) Calculate the translational speed of a...Ch. 10 - (I) A bowling ball of mass 7.3kg and radius 9.0 cm...Ch. 10 - (I) Estimate the kinetic energy of the Earth with...Ch. 10 - (II) A sphere of radius r0 = 24.5 cm and mass m =...Ch. 10 - (II) A narrow but solid spool of thread has radius...Ch. 10 - (II) A ball of radius r0 rolls on the inside of a...Ch. 10 - (II) A solid rubber ball rests on the floor of a...Ch. 10 - (II) A thin, hollow 0.545-kg section of pipe of...Ch. 10 - (II) In Example 1020, (a) how far has the ball...Ch. 10 - (III) The 1100-kg mass of a car includes four...Ch. 10 - (III) A wheel with rotational inertia I=12MR2...Ch. 10 - (III) A small sphere of radius r0 = 1.5 cm rolls...Ch. 10 - (I) A rolling hall slows down because the normal...Ch. 10 - A large spool of rope rolls on the ground with the...Ch. 10 - On a 12.0-cm-diameter audio compact disc (CD),...Ch. 10 - (a) A yo-yo is made of two solid cylindrical...Ch. 10 - A cyclist accelerates from rest at a rate of l.00...Ch. 10 - Suppose David puts a 0.50-kg rock into a sling of...Ch. 10 - A 1.4-kg grindstone in the shape of a uniform...Ch. 10 - Bicycle gears: (a) How is the angular velocity R...Ch. 10 - Figure 1065 illustrates an H2O molecule. The O H...Ch. 10 - One possibility for a low-pollution automobile is...Ch. 10 - A hollow cylinder (hoop) is rolling on a...Ch. 10 - Prob. 93GP Ch. 10 - A marble of mass m and radius r rolls along the...Ch. 10 - The density (mass per unit length) of a thin rod...Ch. 10 - If a billiard ball is hit in just the right way by...Ch. 10 - If the coefficient of static friction between...Ch. 10 - A cord connected at one end to a block which can...Ch. 10 - The radius of the roll of paper shown in Fig. 1070...Ch. 10 - A solid uniform disk of mass 21.0 kg and radius...Ch. 10 - When bicycle and motorcycle riders pop a wheelie,...Ch. 10 - A crucial part of a piece of machinery starts as a...Ch. 10 - A thin uniform stick of mass M and length l is...Ch. 10 - (a) For the yo-yo-like cylinder of Example 1019,...Ch. 10 - (II) Determine the torque produced about the...Ch. 10 - (II) Use the expression that was derived in...

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