Question: A disk rolls without slipping across a horizontal plane. The plane of the disk remains vertical, but it is free to rotate about a vertical

A disk rolls without slipping across a horizontal plane. The plane of the disk remains vertical, but it is free to rotate about a vertical axis. What generalized coordinates may be used to describe the motion? Write a differential equation describing the rolling constraint. Is this equation integrable? Justify your answer by a physical argument. Is the constraint holonomic?

Step by Step Solution

★★★★★

3.39 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Four coordinates are necessary to completely describe the disk Thes... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

P-C-D-H-D (1).docx

120 KBs Word File

Students Have Also Explored These Related Classical Dynamics Of Particles Questions!

A wheel is free to rotate about its fixed axle. A spring is attached to one of its spokes a distance r from the axle, as shown in Figure.(a) Assuming that the wheel is a hoop of mass m and radius R,...

Assuming everything else stays the same, an increase in both our revenue per unit and our variable cost per unit (same dollar amount for both increases): a. will cause our unit breakeven point to...

A 750 g, 50-cm-long metal rod is free to rotate about a frictionless axle at one end. While at rest, the rod is given a short but sharp 1000 N hammer blow at the center of the rod, aimed in a...

Use the following information to answer the question below. Forward Venture Company, which uses a standard cost system, budgeted $500,000 of fixed overhead when 40,000 machine hours were anticipated....

In the context of marginal accounting, what does the term "marginal cost" refer to? A) The total cost incurred for producing a certain quantity of goods. B) The average cost per unit of production....

Question 3 (25 Points) (a) A solid rigid disk has radius R, thickness T and mass m. It is released at rest from a height H (>>R) on the top of a slope which is inclined at an angle of 0 to the ground...

18. [-/10 Points] DETAILS SERPSE10 10.8.OP.026. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The object shown in the figure below consists of a thin rod of length ? = 23.9 cm and mass m = 1.20 kg with...

1. [-/2 Points] DETAILS SERCP11 8.4.P.044. A bicycle wheel has a diameter of 63.0 cm and a mass of 1.73 kg. Assume that the wheel is a n the outside radius. The bicycle is placed on a stationary...

AP CollegeBlamed w : ( 1 ) + 1 2 ( 2 ) ( 4 2 ) Scoring Guide Unit 5.2 Rotational Kinematics (A) 4 radians (B) 16 radians C) 20 radians 8 = 36 D) 24 radians (E) 36 radians V . 8. A disk initially at...

In Figure a small, nonconducting ball of mass m = 1.0 mg and charge q = 2.0 10 8 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle = 30 with a...

Analysis of the bank data reveals that the credits consist of $79,000 of July deposits and a credit memorandum of $3,470 for the collection of a $3,400note plus interest revenue of $70. The July...

Roy's weldting Supplies common stock sells for $ 3 8 a share and pays an annual dividend that increases by 3 percent annually The market rate ofs returtion this stock is 8 . 2 0 percent, what the...

On January 1, 2017, Belgium Industries SA had the following equity accounts. Share Capital-Ordinary (4 par value, 250,000 shares issued and outstanding) Share Premium-Ordinary Retained Earnings...

1.Prior to Risk Management Information Gathering Exercise discussed earlier in the chapter case, consider the challenges of the newly formed project team in undertaking Risk Management in such a...

Power Dispatching at Old Dominion The demand for electricity varies greatly during the day. Because large amounts of electricity cannot be stored economically, electric power companies cannot...

James and Esther Johnson live at 45678 S.W. 112th Street, Homestead, FL 33033. James, who is 67 years old (date of birth 12/14/1952), is retired receiving social security benefits, and Esther, who is...

1. Based on the above facts, which option (lease or buy) minimizes GFWs after-tax cost of obtaining the facility? 2. The local real estate investor has provided an option for GFW to consider. Under...

A 20X objective and 10x eyepiece give an angular magnification of 200x when used in a microscope with a 160 mm tube length. What magnification would this objective and eyepiece give if used in a...

Dalton Company manufactures and sells two products. Relevant per-unit data concerning each product follow: Product Basic Deluxe Selling price $43.00 $53.00 Variable costs $19.00 $27.10 Machine hours...

What is the present value of the below cash flow? Cash flow 100.0 Time to receipt, years 10.0 Discount rate 10.0% Select one: 38.6 90.9 1,000.0 259.4

Which of the following statements is CORRECT? Group of answer choices The factors that affect a firm's business risk are affected by industry characteristics and economic conditions. Unfortunately,...