1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
densk [106]
3 years ago
7

A uniform rod of mass M and length L can pivot freely at one end. Initially, the rod is oriented vertically above the pivot, in

unstable equilibrium, and is released from rest. When the rod is again vertical, below the pivot, what is the speed of its center of mass (in terms of g and L)? The rotational inertia about the end of a uniform rod is 1 3 M L2 .
Physics
1 answer:
Leya [2.2K]3 years ago
4 0

Answer:

The speed of its center of mass =\sqrt{\frac{3}{2}gL}

Explanation:

Consider the potential energy at the level of center of mass of rod below the pivot=0

Mass of uniform rod=M

Length of rod=L

The rotational inertia about the end of a uniform rod=\frac{1}{3}ML^2

Kinetic energy at the level of center of mass of rod below the pivot=\frac{1}{2}I\omega^2

Kinetic energy at the level of center of mass of rod above the pivot=0

Potential energy at the level of center of mass of rod above the pivot=mgh

We have to find the center of mass ( in terms of g and L).

According to conservation of law of energy

Initial P.E+Initial K.E=Final P.E+Final K.E

mgh+0=0+\frac{1}{2} I\omega^2

Where K.E=\frac{1}{2} I\omega^2

I=Moment of inertia

\omega=Angular velocity

Substitute the values then we get

MgL=\frac{1}{2}\times \frac{1}{3}ML^2\omega^2

\omega^2=\frac{6g}{L}

Now, we know that \omega=\frac{v}{r}, r=\frac{L}{2}

Substitute the values then we get

\frac{v^2}{(\frac{L}{2})^2}=\frac{6g}{L}

\frac{v^24}{L^2}=\frac{6g}{L}

v^2=\frac{6g\times L^2}{4L}

v^2=\frac{3gL}{2}

v=\sqrt{\frac{3}{2}gL}

Hence, the speed of its center of mass =\sqrt{\frac{3}{2}gL}

You might be interested in
Any two application of gravity
Brrunno [24]

Answer:

Well the definition of an application is the act of putting to a special use or purpose so lam assuming that you want specific uses that scientists make of gravity in their work.

Well our first application has helped us to send satellites around the solar system with what Nasa calls gravity assist. Using a particular planets gravity to slingshot a satellite to another destination. Look it up.

The next application much simpler but here on Earth. There are many hydro-electric power stations in use all over the world. Water is stored at a high level and released falling 100s of metres to a turbine where it generates electricity.

Hope that helps.

Explanation:

5 0
3 years ago
When an electric current flows through a long conductor, each free electron moves
ki77a [65]
A. through a relatively short distance.

The speed is actually called the drift speed of the electron.
7 0
3 years ago
If a 25 kg lawnmower produces 347 w and does 9514 J of work, for
Igoryamba

Steps 1 and 2)

The variables are W = work, P = power, and t = time. In this case, W = 9514 joules and P = 347 watts.

The goal is to solve for the unknown time t.

-----------------------

Step 3)

Since we want to solve for the time, and we have known W and P values, we use the equation t = W/P

-----------------------

Step 4)

t = W/P

t = 9514/347

t = 27.4178674351586

t = 27.4 seconds

-----------------------

Step 5)

The lawn mower ran for about 27.4 seconds. I rounded to three sig figs because this was the lower amount of sig figs when comparing 9514 and 347.

-----------------------

Note: we don't use the mass at all

6 0
3 years ago
Fehling's solution is added to the counters of test tube b after about 3 minutes and it turns brick red.what food substance was
hjlf

The food substance being used which turned Fehling's solution to brick red is a reducing sugar.

<h3>What is Fehling's solution?</h3>

This is an indicator which is used to test for the presence of reducing sugar or aldehydes in a solution.

Brick red precipitate of copper(I) oxide is formed when it tests positive to compounds such as glucose etc.

Read more about Fehling solution here brainly.com/question/3262179

#SPJ1

6 0
2 years ago
After a collision between two different massed objects; the larger objects accelerate at a faster rate than the smaller object?
Nitella [24]

Answer: Things continue doing what they are doing unless a force is applied to it. Objects have a natural tendency to resist change. This is INERTIA. Heavier objects (objects with more mass) are more difficult to move and stop. Heavier objects (greater mass) resist change more than lighter objects, so true

Explanation:

Pushing a bicycle or a Cadillac, or stopping them once moving. The more massive the object (more inertia) the harder it is to start or stop. The Cadillac has more of a tendency to stay stationary (or continue moving), and resist a change in motion than a bicycle.

6 0
2 years ago
Other questions:
  • Sir Marvin decided to improve the destructive power of his cannon by increasing the size of his cannonballs. Sir Seymour kept hi
    13·1 answer
  • When a force causes an object to move in the direction of the force blank occurs
    7·1 answer
  • A thin coil has 16 rectangular turns of wire. When a current of 3 A runs through the coil, there is a total flux of 4 × 10-3 T·m
    7·1 answer
  • It is too cold<br>for liquid<br>water to exist<br>on the<br>surface.​
    6·1 answer
  • Time Warner Cable's leadership development program that spanned over 30 days and included weekly videos, practice exercises, and
    9·1 answer
  • Find the velociity of a car which travels 35 m to the right over a period of 40 seconds
    12·1 answer
  • TRUE OR FALSE?
    6·1 answer
  • Which of these is a transverse wave? Help pls
    14·2 answers
  • How efficient are the small and large scale solar-power systems used in individual homes and industrial settings?
    5·1 answer
  • I dont know what pfp to put on today so I'm asking u guys....
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!