Online Calculators since 2009
In this Physics tutorial, you will learn:
In tutorial "Moment of Force. Conditions of Equilibrium", we discussed about moment of force or as it is otherwise known, the turning effect of force. However, the focus in that tutorial was setting up the equilibrium of a system, i.e. when the total clockwise moment is numerically equal to its opposite, i.e. the total anticlockwise moment of force.
In this tutorial we will focus on another aspect of turning effect, i.e. when forces "help" each other to make the turning effect easier. Obviosly, they must act in the same direction of rotation.
By definition, "Torque is a non-zero resultant moment of force usually produced by a single force or a couple of forces that help each other when trying to rotate a system around a fixed point."
Torque can be either produced by a single force of by a couple of forces as long as they are able to create rotation in the system. As you see, the meaning of torque is very close to that of moment of force. The most important difference between these two concepts lies in the fact that torque is a movement effect whereas moment of force is a static effect. This means torque is used where there is rotation involved whereas moment of force is used where there is no rotation (when there is equilibrium).
As you can see, all three examples shown above (in the second set of examples), involve the same process: opening a door. Thus, torque is applied three times in a row in this process: turning the key (action 1), turning the door knob (2) and pushing the door as it swings around its hinges (3). Look at the figure.
On the other hand, in the first set of the abovementioned examples, there are two forces acting in the same direction or rotation on both sides of a system. Let's take the steering wheel for illustration.
Both forces applied by our hands help each other making the rotation of steering wheel easier. As a result, the car turns in the desired direction. In the figure below, forces F1 and F2 help each other rotate the steering wheel clockwise. As a result, the car turns right.
In most cases (although it is not a must), the distance from the turning force is the same for each force applied when they form a couple. This helps the users balance their senses. In the specific case, this distance is equal to the radius of the steering wheel.
Both Moment of Force and Torque have the same unit i.e. N-m but The equation of torque for a single force applied is:
where r ⃗ is the distance from the turning point (usually the radius of a circle), and F⃗⊥ is the perpendicular force to the bar (line of action) or the tangent force used at that specific point of the circle.
The scalar equivalent of the above equation is
where θ is the angle between the axis of rotation and the force applied. Look at the figure:
In this figure there is a single force that produce torque. However, not all the force goes for the rotation of the system; some of it is wasted (the component of force in the direction of the bar). Therefore, since only the component of force perpendicular to the bar is able to produce rotation, we consider only it as a turning force.
A 60 N acts at the edge of a bar in the direction shown in the figure.
Giving that cos 400 = 0.766 and sin 400 = 0.643, calculate the length of bar in cm to produce a 10 N × m torque.
From the scalar equivalent of the equation of torque
we obtain after substitutions,
As for the torque of a couple, we obtain the following equation:
When the couple of forces is used to rotate a kind of wheel (such as a steering wheel), we have
A steering wheel has not been lubricated properly and a 12 N force is needed to overcome friction. What is the minimum force a driver must use on the steering wheel with either hand to make the car turn left at 24 N × m? The diameter of steering wheel is 36 cm.
The steering wheel must rotate anticlockwise to make the car turn left. Also, F1 = F2 = F and r1 = r2 = r = d/2 = 36 cm / 2 = 18 cm = 0.18 m.
The torque given in the clues is the resultant (net) torque. It inludes the positive torque produced by the driver and the negative torque of the friction against motion. Therefore, we have
For the negative torque produced by friction, we have
If we take the angle θ = 90° (as we need the minimum values of force), we obtain
Therefore, the torque produced by the driver is
This torque is produced by a couple of equal forces acting at r = 0.18 cm away from the turning point. Thus, we have
Thus,
Therefore, the driver must apply a 72.7 N by either hand to make the system rotate as described.
Remark! As for the signs of the directions of rotation, anticlockwise is taken as positive [clockwise is negative].
By definition, "Torque is a non-zero resultant moment of force usually produced by a single force or a couple of forces that help each other when trying to rotate a system around a fixed point."
Torque can be either produced by a single force of by a couple of forces as long as they are able to create rotation in the system. The meaning of torque is very close to that of moment of force. The most important difference between these two concepts lies in the fact that torque is a movement effect whereas moment of force is a static effect. This means torque is used where there is rotation involved whereas moment of force is used where there is no rotation (when there is equilibrium).
Examples of torque involving a couple of forces include:
Other examples of torque but which involve the use of a single force include:
Both Moment of Force and Torque have the same unit i.e. N-m but The equation of torque for a single force applied is:
where r⃗ is the distance from the turning point (usually the radius of a circle), and F⃗⊥ is the perpendicular force to the bar (line of action) or the tangent force used at that specific point of the circle.
The scalar equivalent of the above equation is
where θ is the angle between the axis of rotation and the force applied.
As for the torque of a couple, we obtain the following equation:
When the couple of forces is used to rotate a kind of wheel (such as a steering wheel), we have r1 = r2 = r
As for the signs of the directions of rotation, anticlockwise is taken as positive [clockwise is negative].
1) Calculate the net torque for the system shown in the figure (take anticlockwise as positive).
What is the net torque of the system if cos 370 = 0.8 and sin 370 = 0.6?
Correct Answer: D
2) Calculate the net torque of the system shown in the figure. (Take anticlockwise as positive)
Correct Answer: A
3) Rank the torques the four forces in the figure produce in the system (greatest first).
Correct Answer: B
We hope you found this Physics tutorial "Torque" useful. If you thought the guide useful, it would be great if you could spare the time to rate this tutorial and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines. In the next Physics section, we expand your insight and knowledge of "Rotation" with our Physics tutorials on Rotation.
The following Physics Calculators are provided in support of the Centre of Mass and Linear Momentum tutorials.
You may also find the following Physics calculators useful.