If a particle with mass m moves with position vector r(t), then its angular momentum is defined
Question:
If a particle with mass m moves with position vector r(t), then its angular momentum is defined as L(t) = mr(t) x v(t) and its torque as τ(t) = mr(t) x a(t).
Show that L'(t) = τ(t). Deduce that if τ(t) = 0 for all t, then L(t) is constant. (This is the law of conservation of angular momentum.)
Step by Step Answer:
Ltmrt x vt L t mr t x vt rt x vt ...View the full answer
Related Video
In Physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. In this video, the concept of force and torque is demonstrated with the practical application of changing the flat tire of the car.
Students also viewed these Mathematics questions
-
An object with mass m moves with position function r(t) = a sin t i + b cos t j + ct k, 0 < t < /2. Find the work done on the object during this time period.
-
The figure shows the path of a particle that moves with position vector r(t) at time t. (a) Draw a vector that represents the average velocity of the particle over the time interval 2 < t < 2.4. (b)...
-
Find the limit, if it exists, or show that the limit does not exist. y sin?x + y* lim (, ) (0, 0) * + *
-
Count Dracula, the most famous vampire, rumored to have killed at least 200,000 people, was based on a real person who lived in eastern Europe about 600 years ago. He was indeed a "monster," although...
-
Knowlton Company had net sales of $3,906,000. Knowlton had the following balances: Required: 1. Calculate the average accounts receivable. 2. Calculate the accounts receivable turnover ratio. 3....
-
Four proposals are under consideration by your company. Proposals A and C are mutually exclusive; proposals B and D are mutually exclusive and cannot be implemented unless proposal A or C has been...
-
What is the most widely followed statistic in business? a. Gross profit b. Earnings per share c. Retained earnings d. Dividends
-
This year, Sigma Inc. generated $612,000 income from its routine business operations. In addition, the corporation sold the following assets, all of which were held for more than 12 months. a....
-
On December 1 of the current year, the following accounts and their balances appear in the ledger of Latte Corp, a coffee processor Preferred 2% Stock $50 par (250,000 shares authorized, 80,000...
-
Zev enters it a contract with Aerin to buy Aerin's boat for $2,500. Zev tells Aerin he plans to use the boat to charge people to travel around the harbor to look at the Christmas lights. Zev has done...
-
The magnitude of the acceleration vector a is 10 cm/s 2 . Use the figure to estimate the tangential and normal components of a.
-
The position function of a spaceship is and the coordinates of a space station are (6, 4, 9). The captain wants the spaceship to coast into the space station. When should the engines be turned off?...
-
Allometry is the area of biology that studies how different parts of a body grow in relation to other parts. Figure 2.62 shows a scatterplot comparing the length and width of petals of irises. Figure...
-
To what extent does the decline of trust in traditional media institutions and the rise of partisan cable news outlets influence voter participation and political polarization in the United States?
-
Tempquin Motors is an all-equity firm with a total market value of $260 million. It's annual before tax operating income (EBIT) is $39.5 million and expected to be stable for the distant future. The...
-
While international trade has lifted millions out of poverty and fostered economic growth, concerns are rising about its impact on income inequality within countries. How can policymakers design...
-
1. Write a pseudocode or flowchart that will compute for ax given a positive integer x. real value a and 2. Write a pseudocode or flowchart that will compute and display the sum of the powers of x...
-
Throughout history, various art movements have challenged existing conventions and definitions of art itself. Considering the Dada movement's use of everyday objects and Marcel Duchamp's famous...
-
Refer to the information in Exercise 4-20. You, business analyst at Second Cup Ltd. have been asked to calculate the debt to equity ratio (round to two decimal places). Provide your manager with...
-
The figure shows a bolted lap joint that uses SAE grade 8 bolts. The members are made of cold-drawn AISI 1040 steel. Find the safe tensile shear load F that can be applied to this connection if the...
-
Determine whether the sequence converges or diverges. If it converges, find the limit. an n+ n3 - 2n
-
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R n (x) 0.] Also find the associated radius of convergence. f(x) = x,...
-
Determine whether the series converges or diverges. 00 n=1 2+ sin n n
-
1. Please briefly indicate and describe the organization you will apply your answers to, such as your employer or another organization you are familiar with. 2. What is marketing? What is marketing...
-
10 In Exercises 5-12, apply Trigonometric Substitution to evaluate the indefinite integrals. vx+1dx 5 6. 1 dx 8 4x+1dx 9x2 dx 16x2 dx 11 dx 12. dx 8
-
Mr A just received a new Amex credit card. It will charge 20.74% p.a. compounding daily if he does not pay off his balance at the end of each month. He went on a shopping spree purchasing $107,489...
Study smarter with the SolutionInn App