Concept explainers
A solid ball and a solid cylinder roll down a ramp. They both start from rest at the same time and place. Which gets to the bottom first?
- They get there at the same time.
- They get there at almost exactly the same time except for frictional differences.
- The ball gets there first.
- The cylinder gets there first.
- Can’t tell without knowing the mass and radius of each.
The body reaching the bottom of the ramp first.
Answer to Problem 1OQ
Solution:
(E). The solid ball, assuming both bodies have the same the radius and the same mass.
Given:
We have a solid sphere and a solid cylinder, but we are not told the radius or the mass. They start to move from rest at the same time and place.
Explanation of Solution
The object with the lower moment of inertia will reach the bottom of the ramp first. The moment of inertia depends on the mass distribution; the closer the mass to the axis, the lower the moment of inertia.
The moment of inertia is calculated with the next equation:
Where r is the distance from the axis to the dm . Solving this equation for the mass distribution of a solid sphere:
Where m is the mass and r is the radius. The moment of inertia for a solid cylinder with an axis passing through its centre:
If we assume, they have the same mass and the same radius, the sphere (the ball) has the lower moment of inertia and it will reach the bottom of the ramp first.
So, correct option is E.
Conclusion:
On two objects that have the same mass and radius, the moment of inertia depends on the mass distribution.
Want to see more full solutions like this?
Chapter 8 Solutions
Physics: Principles with Applications
Additional Science Textbook Solutions
Glencoe Physical Science 2012 Student Edition (Glencoe Science) (McGraw-Hill Education)
Physics for Scientists and Engineers with Modern Physics
College Physics: A Strategic Approach (4th Edition)
The Cosmic Perspective
University Physics (14th Edition)
Tutorials in Introductory Physics
- A student rides his bicycle at a constant speed of 3.00 m/s along a straight, level road. If the bikes tires each have a radius of 0.350 m, (a) what is the tires angular speed? (See Section 7.3.) (b) What is the net torque on each tire? (See Section 8.5.)arrow_forwardA carnival carousel accelerates nonuniformly from rest, moving through an angle of 8.60 rad in 6.00 s. If its turning at 3.30 rad/s at that time, find (a) its average angular speed, and (b) average angular acceleration during that time interval. (See Section 7.1.)arrow_forwardHaileys comet moves about the Sun in an elliptical orbit, with its closest approach to the Sun being 0.59 AU and its greatest distance being 35 AU (1 AU is the Earth-Sun distance). If the comets speed at closest approach is 54 km/s, what is its speed when it is farthest from the Sun? You may neglect any change in the comets mass and assume that its angular momentum about the Sun is conserved.arrow_forward
- Suppose a piece of dust has fallen on a CD. If the spin rate of the CD is 500 rpm, and the piece of dust is 4.3 cm from the center, what is the total distance traveled by the dust in 3 minutes? (Ignore accelerations due to getting the CD rotating.)arrow_forwardAs a compact disc (CD) spins clockwise as seen from above,information is read from it, starting with the innermost ring andmoving outward. When the information is being read from theinnermost ring, the CDs angular speed is 0 = 52.4 rad /s. TheCD slows down so that when information is read from the outermost ring, = 20.9 rad /s. It takes 74 min 33 s to read themusic from a particular CD. Find the constant angular acceleration of the CD.arrow_forwardAndrea and Chuck are riding on a merry-go-round. Andrea rides on a horse at the outer rim of the circular platform, twice as far from the center of the circular platform as Chuck, who rides on an inner horse. When the merry-go-round is rotating at a constant angular speed, Andreas angular speed is (a) twice Chucks (b) the same as Chucks (c) half of Chucks (d) impossible to determine.arrow_forward
- In 2015, in Warsaw, Poland, Olivia Oliver of Nova Scotia broke the world record for being the fastest spinner on ice skates. She achieved a record 342 rev/min, beating the existing Guinness World Record by 34 rotations. If an ice skater extends her aims at that rotation rate, what would be her new rotation rate? Assume she can be approximated by a 45-kg rod that is 1.7 m tall with a radius of 15 cm in the record spin. With her aims stretched take the approximation of a rod of length 130 cm with 10 of her body mass aligned perpendicular to the spin axis. Neglect frictional forces.arrow_forwardWhat if another planet the same size as Earth were put into orbit around the Sun along with Earth. Would the moment of inertia of the system increase, decrease, or stay the same?arrow_forwardThe dung beetle is known as one of the strongest animals for its size, often forming balls of dung up to 10 times their own mass and rolling them to locations where they can be buried and stored as food. A typical dung ball formed by the species K. nigroaeneus has a radius of 2.00 cm and is rolled by the beetle at 6.25 cm/s. (a) What is the rolling balls angular speed? (b) How many full rotations are required if the beetle rolls the ball a distance of 1.00 m?arrow_forward
- A solid, uniform disk of radius 0.250 m and mass 55.0 kg rolls down a ramp of length 4.50 m that makes an angle of 15.0 with the horizontal. The disk starts from rest from the top of the ramp. Find (a) the speed of the disks center of mass when it reaches the bottom of the ramp and (b) the angular speed of the disk at the bottom of the ramp.arrow_forwardA 60.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 500 kg m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clock-wise (as viewed from above the system) at a constant speed of 1.50 m/s relative to Earth. (a) In what direction and with what angular speed does the turntable rotate? (b) How much work does the woman do to set herself and the turntable into motion?arrow_forwardTwo ponies of equal mass are initially at diametrically opposite points on the rim of a large horizontal turntable that is turning freely on a frictionless. vertical axle through its center. The ponies simultaneously start walking toward each other across the turntable, (i) As they walk, what happens to the angular speed of the turntable? (a) It increases, (b) h decreases, (c) It stays constant. (Consider the ponies-turntable system in this process and answer yes or no for the following questions. (ii) Is the mechanical energy of the system conserved? (iii) Is the momentum of the system conserved? (iv) Is the angular momentum of the system conserved?arrow_forward
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill