Torque is the perpendicular force that acts upon an axis at some distance.
When you switch on the fan, it starts rotating, while its center remains unmoved. Since the center of the fan stays at rest, which means the vector sum of all the external forces acting on the fan must be zero. It means one can generate angular acceleration in an object even when an external force is zero.
Well, producing angular acceleration without an external force seems to be an impossible task. However, it is possible with something called the moment of force or the torque due to force. So, what do you mean by torque?
Suppose that you have a car. For driving it, the wheels have to move in the forward direction. Now, take a plank and fix it at the center of the car’s front wheel and put some weight at one end on the plank. Since gravity tries to pull the weight downward, this tilts the plank, and this tilt makes the wheels move.
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So, the perpendicular is the gravitational pull on the weight, the axis is the axis of the wheel on which it rotates, and the distance is the planck's length.
Let’s take another example:
Suppose you want to rotate your toy fan, and if you rotate through a point near to the axis, it doesn’t rotate; however, if you rotate from some distance, the fan rotates. Do you know why?
So what is happening here?
It’s actually you apply perpendicular to the axis of rotation through which the fan rotates. If you apply the force along the axis of rotation, the distance between the axis of rotation, and the point at which you apply force becomes zero because this fan doesn’t rotate.
Since the distance between the axis of rotation and the applied force are perpendicular to each other, they become a cross-product to each other. Therefore, the formula for the torque becomes in the following manner:
て = F x r
て = Torque and it is a vector quantity whose SI unit is N.m
F = perpendicular force
r = distance
Since the cross-product can be written in the Sine angle as;
て = FrSinθ
Where θ = angle between the force and the lever arm.
Now, when you apply the force along the axis of rotation, the angle between the force and the arm becomes 0°, so the torque also becomes zero, i.e.,
て = Fr Sinθ = Fr Sin 0° = 0
And, if applied perpendicularly, then:
て = Fr Sinθ = Fr Sin 90° = 1
There is something, which is referred to as torque, and that is the moment of force. So, what is meant by moment?
A moment or a moment of force is a measure of the ability of the force to cause a body rotate about its axis. The two terms torque and the moment seem to have the same meaning; however, they differ from each other. So, let’s the difference between the two.
When a small amount of work is done in a small time interval dt to rotate an object by angle dθ is:
dW/dt = て dθ/dt ….(1)
The average power associated with the torque is:
P = dW/dt . . . .(2), and
Angular speed in this interval is:
ω = dθ/dt …(3)
From (1) and (2) in (1), we get:
P = てω
So, the power linked to torque is the product of torque and angular speed of the body about the axis of rotation.
Question 1: Why is Rotational Motion Considered the Toughest and an Important Topic in Mechanics?
Answer: Rotational motion is considered the toughest topic because it requires a great intuition with deep subject knowledge. Torque is one of the topics that is preferred not only at school-level exams but also in higher-level exams; that’s why it becomes an important topic in mechanics.
Question 2: To Maintain the Rotation of the Shaft at an Angular Speed of 300 rad/s, and the Engine Should be Offered a Torque of 280 N.m. Determine the Power Required in the Same.
Answer: Given data:
て= 280 N.m
ω = 300 rad/s
To determine: P
So, using these values in P = てω
P = 300 x 280 = 84000 W or 84 kW
Question 3: Why the Handle of a Screw Gauge Made Wide?
Answer: According to the below equation, F ∝ 1/r
て = F x r
To get an effective turning effect of a screw gauge with less effort (applying force), its handle is made wide to keep the distance ‘‘r’ larger.
Question 4: Is Torque a Power?
Torque is the capacity to perform any task, while power is the rate of doing work or applying torque to generate a turning effect in the body.