A rectangle of height 2a and width 2b rests on top of a fixed cylinder of radius
Question:
A rectangle of height 2a and width 2b rests on top of a fixed cylinder of radius R (see Fig.). The moment of inertia of the rectangle around its center is I. The rectangle is given an infinitesimal kick, and then ??rolls?? on the cylinder without slipping. Find the equation of motion for the tilt angle of the rectangle. Under what conditions will the rectangle fall off the cylinder, and under what conditions will it oscillate back and forth? Find the frequency of these smalloscillations.
b R 2a
Step by Step Answer:
We must first find the position of the rectangles CM ...View the full answer
Related Video
Origami helicopter is a simple toy that can be made by folding a piece of paper into a specific shape. When dropped from a height, the helicopter spins as it falls, due to the aerodynamic properties of its design. Origami helicopters rely on principles of aerodynamics and paper engineering to achieve flight. The helicopter blades are designed with a curved surface that creates lift when they rotate, while the weight of the paper and the design of the body create stability during flight. The angle of the blades and the speed of rotation also affect the lift and stability of the helicopter. The shape and size of the paper used in the origami design can impact the overall flight characteristics. In addition, the mass distribution of the helicopter affects its motion. The weight of the helicopter is concentrated in the bottom part of the design, which creates a stable center of gravity. This stability allows the helicopter to spin evenly and smoothly as it falls.
Students also viewed these Mechanics questions
-
Under what conditions will it make practically no difference whether we sample with or without replacement? Give numeric examples.
-
Under what conditions will it be ideal to use one or several of the relative valuation ratios to evaluate a stock?
-
Under what conditions will weighted average and FIFO process costing consistently produce similar equivalent unit costs?
-
Describe An Analysis of the relationship between Employee Engagement, Satisfaction, and Organizational Performance at Enterprise Mobility
-
Jim Dandy Auto Sales uses all types of media to advertise its products (television, radio, newspaper, Internet, and so on). At the end of 2016, the company president, Jim McKinnley, decided that all...
-
Tony Begay, a currency trader for Chicago-based Saguaro Funds, uses the following futures quotes on the British pound () to speculate on the value of the pound. British Pound Futures, US$/pound (CME)...
-
The probability density function of a random variable \(x\) is given by \[p(x)= \begin{cases}0 & \text { for } x <0 \\ 0.5 & \text { for } 0 \leq x \leq 2 \\ 0 & \text { for } x>2\end{cases}\]...
-
Amfac Company manufactures a single product. The company keeps careful records of manufacturing activities from which the following information has been extracted: The companys manufacturing overhead...
-
Shelhorse Corporation produces and sells a single product. Data concerning that product appear below: Selling price Variable expenses Contribution margin Percent of Per Unit $180 Sales 54 $126 100%...
-
Because Natalie has had such a successful first few months, she is considering other opportunities to develop her business. One opportunity is the sale of fine European juicing machines. The owner of...
-
A ladder of length ? and uniform mass density stands on a frictionless floor and leans against a frictionless wall. It is initially held motionless, with its bottom end an infinitesimal distance from...
-
A tube of mass M and length ? is free to swing by a pivot at one end. A mass m is positioned inside the tube at this end. The tube is held horizontal and then released (see Fig). Let ? be the angle...
-
In many cases, EPS is computed based on the parents portion of consolidated net income and parent company shares and convertibles. However, a different process must be used for some business...
-
Using the midpoint formula, calculate elasticity for each of the following changes in demand. Demand for: a. Cashews b. Portable hard drive (4 terabytes) c. 6-gauge copper wire P $7.50 per pound $80...
-
Using the concepts of the substitution effect, leakages, and crowding out discussed in this chapter, discuss whether a small city like Indianapolis or a big city like Los Angeles would benefit more...
-
What does the sampling theorem tell us?
-
Every summer, a large number of the worlds sports economists meet for a conference in a major city in the western United States. If the schedule permits, the economists always try to go to a local...
-
What is the key idea of VLIW processors?
-
A mountain biker is climbing a steep 20 slope at a constant speed. The cyclist and bike have a combined weight of800 N. Referring to Figure 5.11 for guidance, what can you say about the magnitude of...
-
Selected condensed data taken from a recent statement of financial position of Morino Ltd. are as follows. MORINO LTD. Statement of Financial Position (partial) Other current assets...
-
What are the problems facing cross-certification? How are financial institutions attempting to solve them?
-
A stepped shaft of solid circular cross sections (see figure) has length L = 0.80 m, diameter d2 = 40 mm, and diameter d1 = 30 mm. The material is steel with G = 80 GPa. Determine the strain energy U...
-
A cantilever bar of circular cross section and length L is fixed at one end and free at the other (see figure). The bar is loaded by a torque T at the free end and by a distributed torque of constant...
-
Obtain a formula for the strain energy U of the statically indeterminate circular bar shown in the figure. The bar has fixed supports at ends A and B and is loaded by torques 2T0 and T0 at points C...
-
Diaz Company issued $91,000 face value of bonds on January 1, Year 1. The bonds had a 9 percent stated rate of interest and a ten- year term. Interest is paid in cash annually, beginning December 31,...
-
Manvir had to make payments of $1,125 every 6 months to settle a $22,000 loan that he received at 4.52% compounded semi-annually. a. How long did it take to settle the loan?
-
If I invest a single amount of $14,000 in an account earning 8% p.a. compounding quarterly for 5 years, how much interest will I have earned in those 5 years?
Study smarter with the SolutionInn App