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 43P: A circular disk of radius 10 cm has a contant angular acceleration of 1.0rad/s2 ; at t=0 its angular...
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Concept explainers
A particle starts from rest and moves in a circle with a radius of 1 m. Its angular position is given by the equation ø = 3.0t -1.0t^2 +2.0t^3 where t is in seconds and the angle is in radians. First, determine the instantaneous angular velocity and angular acceleration at 2.00 seconds. Second, determine the tangential acceleration and radial acceleration at that time.
Transcribed Image Text: A particle starts from rest and moves in a circle with a radius of 1.00 m. Its angular
position is given by the equation:
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where tis in seconds and the angle is in radians.
First, determine the instantaneous angular velocity and angular acceleration at 2.00
seconds.
Second, determine the tangential acceleration and radial acceleration at that time.
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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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