We give a strategy for using this equation when analyzing rotational motion.
Problem-solving strategy: work-energy theorem for rotational motion
Identify the forces on the body and draw a free-body diagram. Calculate the torque for each force.
Calculate the work done during the body’s rotation by every torque.
Apply the work-energy theorem by equating the net work done on the body to the change in rotational kinetic energy.
Let’s look at two examples and use the work-energy theorem to analyze rotational motion.
Rotational work and energy
A
torque is applied to a flywheel that rotates about a fixed axis and has a moment of inertia of
. If the flywheel is initially at rest, what is its angular velocity after it has turned through eight revolutions?
Strategy
We apply the work-energy theorem. We know from the problem description what the torque is and the angular displacement of the flywheel. Then we can solve for the final angular velocity.
Solution
The flywheel turns through eight revolutions, which is
radians. The work done by the torque, which is constant and therefore can come outside the integral in
[link] , is
We apply the work-energy theorem:
With
, we have
Therefore,
This is the angular velocity of the flywheel after eight revolutions.
Significance
The work-energy theorem provides an efficient way to analyze rotational motion, connecting torque with rotational kinetic energy.
A string wrapped around the pulley in
[link] is pulled with a constant downward force
of magnitude 50 N. The radius
R and moment of inertia
I of the pulley are 0.10 m and
, respectively. If the string does not slip, what is the angular velocity of the pulley after 1.0 m of string has unwound? Assume the pulley starts from rest.
Strategy
Looking at the free-body diagram, we see that neither
, the force on the bearings of the pulley, nor
, the weight of the pulley, exerts a torque around the rotational axis, and therefore does no work on the pulley. As the pulley rotates through an angle
acts through a distance
d such that
Solution
Since the torque due to
has magnitude
, we have
If the force on the string acts through a distance of 1.0 m, we have, from the work-energy theorem,
Power always comes up in the discussion of applications in engineering and physics. Power for rotational motion is equally as important as power in linear motion and can be derived in a similar way as in linear motion when the force is a constant. The linear power when the force is a constant is
. If the net torque is constant over the angular displacement,
[link] simplifies and the net torque can be taken out of the integral. In the following discussion, we assume the net torque is constant. We can apply the definition of power derived in
Power to rotational motion. From
Work and Kinetic Energy , the instantaneous power (or just power) is defined as the rate of doing work,
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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