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
Question
Chapter 7, Problem 7.1P
To determine
The generalized coordinates and description about the rolling disk.
Expert Solution & Answer
Answer to Problem 7.1P
The generalized coordinates and description about the rolling disk are given.
Explanation of Solution
In order to describe the rolling of disk without slipping, four generalized coordinates are required. They are – x coordinate, y coordinate, angle
Equation of motion for the rolling disk is,
Here,
These equations are not integrable. Moreover, all the generalized coordinates cannot be combined into a single equation. Hence, the constraints are nonholonomic.
Conclusion:
Therefore, generalized coordinates and description about the rolling disk are given.
Want to see more full solutions like this?
Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
As. 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 smallest
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?
Prove the property of the cross product u × v = 0 if and only if u and v are scalar multiples of each other.
Chapter 7 Solutions
Classical Dynamics of Particles and Systems
Knowledge Booster
Similar questions
- For any arbitrary vectors u, v and w, prove thatarrow_forwardNote: Because the arguments of the trigonometric functions are unitless in this question, your calculator must be in radian mode if you use it to evaluate any trigonometric functions. When powered up, a disk drive starts at rest and spins up with non-uniform angular acceleration according to the following formula: =asin(bt) where a = 708 radians/s2 and b = 1.74 s-1. This lasts for the first 1.81 seconds, after which the drive does not accelerate. How many meters of disk surface have passed underneath the head in 0.79 seconds?arrow_forward(The complete question is in the picture) Three identical point masses are arranged to an equilateral triangle as shown. Let point P be the center of the triangle formed by the masses, Q be located at one vertex of the triangle, and S be the midpoint of the line joining two of the three masses. Consider thefollowing orientations where the axis of rotation of the triangle can be located:I. out of the page, passing through PII. along the line `III. out of the page, passing through QIV. out of the page, passing through SHow would you rank them in terms of increasing moment of inertia? A. II, III, IV, IB. II, I, III, IVC. II, III, I, IVD. II, I, IV, IIIarrow_forward
- Consider a vector Q that rotates at angular frequency ω about some fixed axis of rotation (~ω).Further, Q is at a fixed angle α relative to that axis. Show that the time rate of change of Q is given byarrow_forwardIf 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.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
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning