University Physics Volume 1 18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: William Moebs, Samuel J. Ling, Jeff Sanny
1 Units And Measurement 2 Vectors 3 Motion Along A Straight Line 4 Motion In Two And Three Dimensions 5 Newton's Law Of Motion 6 Applications Of Newton's Laws 7 Work And Kinetic Energy 8 Potential Energy And Conservation Of Energy 9 Linear Momentum And Collisions 10 Fixed-axis Rotation 11 Angular Momentum 12 Static Equilibrium And Elasticity 13 Gravitation 14 Fluid Mechanics 15 Oscillations 16 Waves 17 Sound Chapter10: Fixed-axis Rotation
Chapter Questions Section: Chapter Questions
Problem 10.1CYU: Check Your Understanding The fan blades on a turbofan jet engine (shown below) accelerate from rest... Problem 10.2CYU: Check Your Understanding A centrifuge used in DNA extraction spins at a maximum rate of 7000 rpm,... Problem 10.3CYU: Check Your Understanding A boy jumps on a merry-go-round with a radius of 5 m that is at rest. It... Problem 10.4CYU: Check Your Understanding A nuclear submarine propeller has a moment of inertia of 800.0kgm2 . If the... Problem 10.5CYU: Check Your Understanding What is the moment of inertia of a cylinder of radius R and mass m about an... Problem 10.6CYU: Check Your Understanding A large ocean-going ship runs aground near the coastline, similar to the... Problem 10.7CYU: Check Your Understanding The fan blades on a jet engine have a moment of inertia 30.0kgm2 . In 10s,... Problem 10.8CYU: Check Your Understanding A constant torque of 500kNm is applied to a wind turbine to keep it... Problem 1CQ: A clock is mounted on the wall. As you look at it, what is the direction of the angular velocity... Problem 2CQ: What is the value of the angular acceleration of the second hand of the clock on the wall? Problem 3CQ: A baseball bat is swung. Do all points on the bat have the same angular velocity? The same... Problem 4CQ: The blades of a blender on a counter are rotating clockwise as you look into it from the top. If the... Problem 5CQ: If a rigid body has a constant angular acceleration, what is the functional form of the angular... Problem 6CQ: If a rigid body has a constant angular acceleration, what is the functional form of the angular... Problem 7CQ: If the angular acceleration of a rigid body is zero, what is the functional form of the angular... Problem 8CQ: A massless tether with a masses tied to both ends rotates about a fixed axis through the center. Can... Problem 9CQ: Explain why centripetal acceleration changes the direction of velocity in circular motion but not... Problem 10CQ: In circular motion, a tangential acceleration can change the magnitude of the velocity but not its... Problem 11CQ: Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it experience... Problem 12CQ: What if another planet the same size as Earth were put into orbit around the Sun along with Earth.... Problem 13CQ: A solid sphere is rotating about an axis through its center at a constant rotation rate. Another... Problem 14CQ: If a child walks toward the center of a merry-go-round, does the moment of inertia increase or... Problem 15CQ: A discus thrower rotates with a discus in his hand before letting it go. (a) How does his moment of... Problem 16CQ: Does increasing the number of blades on a propeller increase or decrease its moment of inertia, and... Problem 17CQ: The moment of inertia of a long rod spun around an axis through one end perpendicular to its length... Problem 18CQ: Why is the moment of inertia of a hoop that has a mass M and a radius R greater than the moment of... Problem 19CQ: What three factors affect the torque created by a force relative to a specific pivot point? Problem 20CQ: Give an example in which a small force exerts a large torque. Give another example in which a large... Problem 21CQ: When reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of... Problem 22CQ: Can a single force produce a zero torque? Problem 23CQ: Can a set of forces have a net torque that is zero and a net force that is not zero? Problem 24CQ: Can a set of forces have a net force that is zero and a net torque that is not zero? Problem 25CQ Problem 26CQ: If you were to stop a spinning wheel with a constant force, where on the wheel would you apply the... Problem 27CQ Problem 28P: Calculate the angular velocity of Earth. Problem 29P: A track star runs a 400-m race on a 400-m circular track in 45 s. What is his angular velocity... Problem 30P: A wheel rotates at a constant rate of 2.0103rev/min . (a) What is its angular velocity in radians... Problem 31P: A particle moves 3.0 m along a circle of radius 1.5 m. (a) Through what angle does it rotate? (b) If... Problem 32P: A compact disc rotates at 500 rev/min. If the diameter of the disc is 120 mm, (a) what is the... Problem 33P: Unreasonable results. The propeller of an aircraft is spinning at 10 rev/s when the pilot shuts off... Problem 34P: A gyroscope slows from an initial rate of 32.0 rad/s at a rate of 0.700rad/s2 . How long does it... Problem 35P: On takeoff, the propellers on a UAV (unmanned aerial vehicle) increase their angular velocity form... Problem 36P: The angular position of a rod varies as 20.0t2radians from time t=0 . The rod has two beads on it as... Problem 37P: A wheel has a constant angular acceleration of 5.0rad/s2 . Starting from rest, it turns through 300... Problem 38P: During a 6.0-s time interval, a fly-wheel with a constant angular acceleration turns through 500... Problem 39P: The angular velocity of a rotating rigid body increases from 500 to 1500 rev/min in 120 s. (a) What... Problem 40P: A flywheel slows from 600 to 400 rev/min while rotating through 40 revolutions. (a) What is the... Problem 41P: A wheel 1.0 m in diameter rotates with an angular acceleration of 4.0rad/s2 . (a) If the wheel’s... Problem 42P: A vertical wheel with a diameter of 50 cm starts from rest and rotates with a constant angular... Problem 43P: A circular disk of radius 10 cm has a contant angular acceleration of 1.0rad/s2 ; at t=0 its angular... Problem 44P: The angular velocity vs. time for a fan on a hovercraft is shown below. (a) What is the angle... Problem 45P: A rod of length 20 cm has two beads attached to its ends. The rod with beads starts rotating from... Problem 46P: At its peak, a tornado is 60.0 m in diameter and carries 500 km/h winds. What is its angular... Problem 47P: A man stands on a merry-go-round that is rotating at 2.5 rad/s. If the coefficient of static... Problem 48P: An ultracentrifuge accelerates from to 100,000 rpm in 2.00 min. (a) What is the average angular... Problem 49P: A wind turbine is rotating conterclockwise at 0.5 rev/s and slows to a stop in 10 s. Its blades are... Problem 50P: What is (a) the angular speed and (b) the linear speed of a point on Earth’s surface at latitude 30N... Problem 51P: A child with mass 40 kg sits on the edge of a merry-go-round at a distance of 3.0 m from its axis of... Problem 52P: A bicycle wheel with radius 0.3 m rotates from rest to 3 rev/s in 5 s. What is the magnitude and... Problem 53P: The angular velocity of a flywheel with radius 1.0 m varies according to (t)=2.0t . Plot ac(t) and... Problem 54P: A system of point particles is shown in the following figure. Each particle has mass 0.3 kg and they... Problem 55P: (a) Calculate the rotational kinetic energy of Earth on its axis. (b) What is the rotational kinetic... Problem 56P: Calculate the rotational kinetic energy of a 12-kg motorcycle wheel if its angular velocity is 120... Problem 57P: A baseball pitcher throws the ball in a motion where there is rotation of the forearm about the... Problem 58P: A diver goes into a somersault during a dive by tucking her limbs. If her rotational kindetic energy... Problem 59P: An aircraft is coming in for a landing at 300 meters height when the propeller falls off. The... Problem 60P: If air resistance is present in the preceding problem and reduces the propeller’s rotational kinetic... Problem 61P: A neutron star of mass 21030kg and radius 10 km rotates with a period of 0.02 seconds. What is its... Problem 62P: An electric sander consisting of a rotating disk of mass 0.7 kg and radius 10 cm rotates at 15... Problem 63P: A system consists of a disk of mass 2.0 kg and radius 50 cm upon which is mounted an annular... Problem 64P: While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the... Problem 65P: Using the parallel axis theorem, what is the moment of inertia of the rod of mass m about the axis... Problem 66P: Find the moment of inertia of the rod in the previous problem by direct integration. Problem 67P: A uniform rod of mass 1.0 kg and length 2.0 m is free to rotate about one end (see the following... Problem 68P: A pendulum consists of a rod of mass 2 kg and length 1 m with a solid sphere at one end with mass... Problem 69P: A solid sphere of radius 10 cm is allowed to rotate freely about an axis. The sphere is given a... Problem 70P: Calculate the moment of inertia by direct integration of a thin rod of mass M and length L about an... Problem 71P: Two flywheel fo negligible mass and different radii are bounded together and rotate about common... Problem 72P: The cylindrical head bolts on a car are to be tightened with a torque of 62.0Nm . If a mechanic uses... Problem 73P: (a) When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of... Problem 74P: When tightening a bolt, you push perpendicularly on a wrench with a force of 165 N at a distance of... Problem 75P: What hanging mass must be placed on the cord to keep the pulley from rotating (see the following... Problem 76P: A simple pendulum consists of a massless tether 50 cm in length connected to a pivot and a small... Problem 77P: Calculate the torque about the z-axis that is out of the page at the origin in the following figure,... Problem 78P: A seesaw has length 10.0 m and uniform mass 10.0 kg and is resting at an angle of 30 with respect to... Problem 79P: A pendulum consists ofa rod of mass 1 kg and length 1 m connected to a pivot with a solid sphere... Problem 80P: A torque of 5.00103Nm is required to raise a drawbridge (see the following figure). What is the... Problem 81P: A horizontal beam of length 3 m and mass 2.0 kg has a mass of 1.0 kg and width 0.2 m sitting at the... Problem 82P: What force must be applied to end of a rod along the x-axis of length 2.0 m in order to produce a... Problem 83P: What is the torque abot the origin of the force if it is applied at the point whose position is: Problem 84P: You have a grindstone (a disk) that is 90.0 kg, has a 0.340-m radius, and is turning at 90.0 rpm,... Problem 85P: Suppose you exert a force of 180 N tangential to a 0.280-m-radius, 75.0-kg grindstone (a solid... Problem 86P: A flywheel (l=50kgm2) starting from rest acquires an angular velocity of 200.0 rad/s while subject... Problem 87P: A constant torque is applied to a rigid body whose moment of inertia is 4.0kgm2 around the axis of... Problem 88P: A torque of 50.0Nm is applied to a grinding wheel (l=20.0kgm2) for 20 s. (a) If it starts from rest,... Problem 89P: A flywheel (I=100.0kgm2) rotating at 500.0 rev/min is brought to rest by friction in 2.0 min. What... Problem 90P: A uniform cylindrical grinding wheel of mass 50.0 kg and diameter 1.0 m is turned on by an electric... Problem 91P: Suppose when Earth was created, it was not rotating. However, after the application of a uniform... Problem 92P: A pulley of moment of inertia 2.0kgm2 is mounted on a wall as shown in the following figure. Light... Problem 93P: A block of mass 3 kg slides down an inclined plane at an angle of 45 with a massless tether attached... Problem 94P: The cart shown below moves across the table top as the block falls. What is the acceleration of the... Problem 95P: A uniform rod of mass and length is held vertically by two strings of negligible mass, as shown... Problem 96P: A thin stick of mass 0.2 kg and length L=0.5m is attached to the rim of a metal disk of mass M=2.0kg... Problem 97P: A wind turbine rotates at 20 rev/min. If its power output is 2.0 MW, what is the torque produced on... Problem 98P: A clay cylinder of radius 20 cm on a potter’s wheel spins at a constant rate of 10 rev/s. The potter... Problem 99P: A uniform cylindrical grindstion has a mass of 10 kg and a radius of 12 cm. (a) What is the... Problem 100P: A uniform disk of mass 500 kg and radius 0.25 m is mounted on frictionless bearings so it can rotate... Problem 101P: A propeller is accelerated from rest to an angular velocity of 1000 rev/min over a period of 6.0... Problem 102P: A sphere of mass 1.0 kg and radius 0.5 m is attached to the end of a massless rod of length 3.0 m.... Problem 103P: A uniform rod of length L and mass M is held vertically with one end resting on the floor as shown... Problem 104P: An athlete in a gym applies a constant force of 50 N to the pedals of a bicycle to keep the rotation... Problem 105P: A 2-kg block on a frictionless inclined plane at 45 has a cord attached to a pulley of mass 1 kg and... Problem 106P: Small bodies of mass m1 and m2 are attached to opposite ends of a thin rigid rod of length L and M.... Problem 107AP: A cyclist is riding such that the wheels of the bicycle have a rotation rate of 3.0 rev/s. If the... Problem 108AP: Calculate the angular velocity of the orbital motion of Earth around the Sun. Problem 109AP: A phonograph turntable rotating at 331/3rev/min slows down and stops in 1.0 min. (a) What is the... Problem 110AP: With the aid of a string, a gyroscope is accelerated from rest to 32 rad/s in 0.40 s under a... Problem 111AP: Suppose a piece of dust has fallen on a CD. If the spin rate of the CD is 500 rpm, and the piece of... Problem 112AP: A system of point particles is rotating about a fixed axis at 4 rev/s. The particles are fixed with... Problem 113AP: Calculate the moment of inertia of a skater given the following information. (a) The 60.0-kg skater... Problem 114AP: A stick of length 1.0 m and mass 6.0 kg is free to rotate about a horizontal axis through the... Problem 115AP: A pendulum consists of a rod of length 2 m and mass 3 kg with a solid sphere of mass 1 kg and radius... Problem 116AP: Calculate the torque of the 40-N force around the axis through O and perpendicular to the plane of... Problem 117AP: Two children push on opposite sides of a door during play. Both push horizontally and perpendicular... Problem 118AP Problem 119AP: An automobile engine can produce 200Nm of torque. Calculate the angular acceleration produced if... Problem 120AP: A grindstone with a mass of 50 kg and radius 0.8 m maintains a constant rotation rate of 4.0 rev/s... Problem 121CP: The angular acceleration of a rotating rigid body is given by =(2.0-3.0t)rad/s2 . If the body starts... Problem 122CP: Earth’s day has increased by 0.002 s in the last century. If this increase in Earth’s period is... Problem 123CP: A disk of mass m , radius R , and area A has a surface mass density =mrAR (see the following... Problem 124CP: Zorch, an archenemy of Rotation Man, decides to slow Earth’s rotation to once per 28.0 h by exerting... Problem 125CP: A cord is wrapped around the rim of a solid cylinder of radius 0.25 m, and a constant force of 40 N... Problem 41P: A wheel 1.0 m in diameter rotates with an angular acceleration of 4.0rad/s2 . (a) If the wheel’s...
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Concept explainers
The angular position of a point on a rotating wheel is given by θ = 4.96 + 1.72t 2 + 2.06t 3 , where θ is in radians and t is in seconds. At t = 0, what are (a) the point's angular position and (b) its angular velocity ? (c) What is its angular velocity at t = 5.16 s? (d) Calculate its angular acceleration at t = 1.05 s. (e) Is its angular acceleration constant?
Transcribed Image Text: The angular position of a point on a rotating wheel is given by e = 4.96 + 1.72t2 + 2.06t³, where e is in
radians and t is in seconds. At t = 0, what are (a) the point's angular position and (b) its angular
velocity? (c) What is its angular velocity at t = 5.16 s? (d) Calculate its angular acceleration at t = 1.05 s.
(e) Is its angular acceleration constant?
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Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
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