Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
error_outline
This textbook solution is under construction.
Students have asked these similar questions
If a particle be describing an ellipse about a centre of force in the centre, show that the
sum of the reciprocates of its angular velocities about foci is constant.
For a particle of mass m and situated at position r from the origin, show that the moment fo force(torque) is given by:
torque = dL / dt
where L is the angular momentum
Hence, show that for a conservative system, L is constant.
Consider the coordinate system in the diagram bellow; the z axis points out of the page. At the point (-d, 0, 0) a ball of mass m is initially (at t= 0) at rest, but it is dropped under the face of gravity, near the Earth. We ignore air resistance as usual, and treat ball as a point mass.
1.c) What is the angular momentum relative to the origin of the coordinate system?
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- What do we get if we multiply the angular momentum raising and lowering operators together?arrow_forwardProblem 7.26 A particle of mass m and angular momentum moves in a central spring-like force field F = −kr. (a) Sketch the effective potential energy Ueff(r). (b) Find the radius r0 of circular orbits. (c) Find the period of small oscillations about this orbit, if the particle is perturbed slightly from it. (d) Compare with the period of rotation of the particle about the center of force. Is the orbit closed or open for such small oscillations?arrow_forwardA point particle moves in space under the influence of a force derivablefrom a generalized potential of the formU(r, v) = V (r) + σ · L,where r is the radius vector from a fixed point, L is the angular momentumabout that point, and σ is the fixed vector in space. Find the components of the force on the particle in spherical polar coordinates, on the basis of the equation for the components of the generalized force Qj: Qj = −∂U/∂qj + d/dt (∂U/∂q˙j)arrow_forward
- Determine the angular momentum Ho of each of the two particles about point o. Use a scalar solution.arrow_forwardAs. 2 Aball of mass m moves along a thread that rotates around one end at an angular velocity ω. The thread is at an angle α with respect to the axis of rotation. Using Lagrange's equations, find the equations of motion of mass along the thread and the time it takes for the ball to slide with nor if it starts from a state of rest at the top. b) Find the curve that connects two points in a plane and its length is the smallestarrow_forwardThe angular moomentum of a point with a mass of m, a velocity v, and position r is: L = mr x v. Prove that the rate of change of L, dL/dt is equal to the torque (T = r x F). F is the force on the point.arrow_forward
- Consider the Lennard-Jones potential between atoms in a solid material. Find the dependence of the equilibrium postion x0, on the parameters in the potential. Then for small perturbations, δx around x0, determine the restoring force as a function of δx.arrow_forwardShow that: If a particle is subject to a central force only, then its angular momentum is conserved i.e. If V(r) = V(r), then dL/dt = 0.arrow_forward(Please explain)In a collision of disks, where the system is not isolated because of the existence of friction. How is it possible that conservation of angular momentum is still valid to a relatively good accuracy?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning