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Calculating torque on a rigid body

[link] shows several forces acting at different locations and angles on a flywheel. We have | F 1 | = 20 N , | F 2 | = 30 N , | F 3 | = 30 N , and r = 0.5 m . Find the net torque on the flywheel about an axis through the center.

Figure shows a flywheel with three forces acting on it at different locations and angles. Force F3 is applied at the center and is perpendicular to the axis of rotation. Force F2 is applied at the left edge and is perpendicular to the axis of rotation. Force F1 is applied at the center and forms 30 degree angle with the axis of rotation.
Three forces acting on a flywheel.


We calculate each torque individually, using the cross product, and determine the sign of the torque. Then we sum the torques to find the net torque.


We start with F 1 . If we look at [link] , we see that F 1 makes an angle of 90 ° + 60 ° with the radius vector r . Taking the cross product, we see that it is out of the page and so is positive. We also see this from calculating its magnitude:

| τ 1 | = r F 1 sin 150 ° = 0.5 m ( 20 N ) ( 0.5 ) = 5.0 N · m .

Next we look at F 2 . The angle between F 2 and r is 90 ° and the cross product is into the page so the torque is negative. Its value is

| τ 2 | = r F 2 sin 90 ° = −0.5 m ( 30 N ) = −15.0 N · m .

When we evaluate the torque due to F 3 , we see that the angle it makes with r is zero so r × F 3 = 0 . Therefore, F 3 does not produce any torque on the flywheel.

We evaluate the sum of the torques:

τ net = i | τ i | = 5 15 = −10 N · m .


The axis of rotation is at the center of mass of the flywheel. Since the flywheel is on a fixed axis, it is not free to translate. If it were on a frictionless surface and not fixed in place, F 3 would cause the flywheel to translate, as well as F 1 . Its motion would be a combination of translation and rotation.

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Check Your Understanding A large ocean-going ship runs aground near the coastline, similar to the fate of the Costa Concordia , and lies at an angle as shown below. Salvage crews must apply a torque to right the ship in order to float the vessel for transport. A force of 5.0 × 10 5 N acting at point A must be applied to right the ship. What is the torque about the point of contact of the ship with the ground ( [link] )?

Figure shows a ship that lies at an angle on the seashore. A force of 50000 N is applied at 10 degree angle to the normal at a point that 100 meters above the point of contact between the ship and the seashore.
A ship runs aground and tilts, requiring torque to be applied to return the vessel to an upright position.

The angle between the lever arm and the force vector is 80 ° ; therefore, r = 100 m(sin80 ° ) = 98.5 m .

The cross product τ = r × F gives a negative or clockwise torque.

The torque is then τ = r F = −98.5 m ( 5.0 × 10 5 N ) = −4.9 × 10 7 N · m .

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  • The magnitude of a torque about a fixed axis is calculated by finding the lever arm to the point where the force is applied and using the relation | τ | = r F , where r is the perpendicular distance from the axis to the line upon which the force vector lies.
  • The sign of the torque is found using the right hand rule. If the page is the plane containing r and F , then r × F is out of the page for positive torques and into the page for negative torques.
  • The net torque can be found from summing the individual torques about a given axis.

Conceptual questions

What three factors affect the torque created by a force relative to a specific pivot point?

magnitude of the force, length of the lever arm, and angle of the lever arm and force vector

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Give an example in which a small force exerts a large torque. Give another example in which a large force exerts a small torque.

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When reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations than would an identical reduction in the mass of the bicycle’s frame?

The moment of inertia of the wheels is reduced, so a smaller torque is needed to accelerate them.

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Questions & Answers

two particles rotate in a rigid body then acceleration will be ?
kinza Reply
same acceleration for all particles because all prticles will be moving with same angular velocity.so at any time interval u find same acceleration of all the prticles
what is electromagnetism
David Reply
It is the study of the electromagnetic force, one of the four fundamental forces of nature. ... It includes the electric force, which pushes all charged particles, and the magnetic force, which only pushes moving charges.
what is units?
Subhajit Reply
units as in how
What is th formular for force
Joseph Reply
F = m x a
State newton's second law of motion
Seth Reply
can u tell me I cant remember
force is equal to mass times acceleration
The acceleration of a system is directly proportional to the and in the same direction as the external force acting on the system and inversely proportional to its mass that is f=ma
The uniform seesaw shown below is balanced on a fulcrum located 3.0 m from the left end. The smaller boy on the right has a mass of 40 kg and the bigger boy on the left has a mass 80 kg. What is the mass of the board?
Asad Reply
Consider a wave produced on a stretched spring by holding one end and shaking it up and down. Does the wavelength depend on the distance you move your hand up and down?
Sohail Reply
no, only the frequency and the material of the spring
how to read physics ncert?
beat line read important. line under line
how can one calculate the value of a given quantity
Helen Reply
To determine the exact value of a percent of a given quantity we need to express the given percent as fraction and multiply it by the given number.
briefly discuss rocket in physics
Ibrahim Reply
ok let's discuss
What is physics
Nura Reply
physics is the study of natural phenomena with concern with matter and energy and relationships between them
a potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inductance of the inductor that should be connected to the capacitor for the circuit to oscillate at 1125Hza potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inducta
Royalty Reply
L= 0.002H
how did you get it?
is the magnetic field of earth changing
tibebeab Reply
what is thought to be the energy density of multiverse and is the space between universes really space
can you explain it
Energy can not either created nor destroyed .therefore who created? and how did it come to existence?
Suzana Reply
this greatly depend on the kind of energy. for gravitational energy, it is result of the shattering effect violent collision of two black holes on the space-time which caused space time to be disturbed. this is according to recent study on gravitons and gravitational ripple. and many other studies
and not every thing have to pop into existence. and it could have always been there . and some scientists think that energy might have been the only entity in the euclidean(imaginary time T=it) which is time undergone wick rotation.
What is projectile?
Nana Reply
An object that is launched from a device
2 dimensional motion under constant acceleration due to gravity
Not always 2D Awais
no comments
why not? a bullet is a projectile, so is a rock I throw
bullet travel in x and y comment same as rock which is 2 dimensional
no all pf you are wrong. projectile is any object propelled through space by excretion of a force which cease after launch
for awais, there is no such thing as constant acceleration due to gravity, because gravity change from place to place and from different height
it is the object not the motion or its components
where are body center of mass on present.
Balwant Reply
on the mid point
is the magnetic field of the earth changing?
does shock waves come to effect when in earth's inner atmosphere or can it have an effect on the thermosphere or ionosphere?
and for the question from bal want do you mean human body or just any object in space
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