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Torque is the moment of force that enables a body to rotate on its own axis and gain angular acceleration. The SI unit of Torque is N.m. It is a vector quantity and can be both static and dynamic. In the following sections, we will learn about moment of force or torque, units of torque, importance of torque and application of torque in detail.
Check also: Class 11 Physics Chapter 7 System of Particles and Rotational Motion
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Keyterms: Torque, Force, Angular acceleration, Acceleration, N.m, Linear force, Rotational effect, Moment of force, Moment, Rotation, Law of Motion
Torque
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Torque can be defined as the rotational equivalent of linear force. The point at which the object rotates is called the axis of rotation.
Torque is also known as turning effect, rotational effect, a moment of force, or moment.
If the magnitude of a body is lower than the movement of an object over a specific distance then it is known as a point object. The motion of the point objects is described in one, two, and three dimensions with the help of kinematics. The point objects are made up of usually very large particles. The rotational behavior of these boundless particles is described by Newton's Law of Motion.
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Formula of Torque
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- Torque = force x distance
- Torque = rF sin θ
Where, r= radius
F = force
θ = angle between lever arm
Formula of Torque
Different units of Torque
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- The SI unit of torque is newton-meter.
- The SI base unit of torque is kgm2sec-2 .
- The non-SI unit of torque is meter-kilogram-force
- In the CGS system, the unit of Torque is dyne-centimeter (dyne-cm)
- Other units of Torque are-
- inch-pound-force
- foot-pounds-force
- ounce-force-inches(ozf.in)
- pounce-force-feet (lbf.ft)
Applications of Torque in Real Life
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- Lock and key
The twisting motion that is put inside a lock to open it is created by torque.
- Ferris wheel
The torque is responsible for rotating the wheel on its axis by pushing the wheel to make the rotation
- Old telephone
The clockwise and anticlockwise rotation of the numbers on a dial happens because of torque with the help of our fingers.
- Gyroscopes
A gyroscope has a flywheel which is a wheel-like disk situated on an axle. Torque creates a rotation in the axis of the flywheel and it is perpendicular to the rotor axis.
- Seesaws
Seesaws display the working of the two most important components of the torque- force and moment arm. The pivot point of the seesaw is the balance point. The person with a heavyweight can reduce the torque by sitting closer to the point and vice versa.
- Hinged doors
Torque is the reason for the hinged door to open and close where the hinge is the pivot point. The door will not open if you apply force near its hinges because there is not enough torque force to open it.
Importance of Torque
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- Torque explains the concept of the rotational motion of rigid bodies.
- The direction and intention of the force applied to a body can be detected by the concept of torque.
- It also determines the clockwise and anti-clockwise motion on a body.
- Torque also determines the angular acceleration when a body rotates.
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Things to Remember
- Torque helps to create angular acceleration in a body rather than creating uniform rotation
- More the force and distance, the larger is the torque created.
- Torque is the moment of force that is applied to the rotational axis, directing at the center of the object.
- Torque is also known as turning effect, rotational effect, a moment of force, or moment.
- The SI unit of torque is newton-meter.
- The SI base unit of torque is kgm2sec-2 and meter-kilogram-force
- In the CGS system, the unit of Torque is dyne-centimeter (dyne-cm)
- Other units of Torque are: inch-pound-force, foot-pounds-force, ounce-force-inches(ozf.in) and pounce-force-feet (lbf.ft).
Sample Questions
Ques: Why do screwdrivers have wide handles? (2 Marks)
Ans: The force and direction from the axis of rotation are equal to the torque which is the turning moment of force. To produce the required moment of force, a small amount of force will be required because of the large distance of the object from the axis of rotation. This is the reason why the handle of the screwdrivers is made wider.
Ques: Explain static torque. Give examples of static torque. (2 Marks)
Ans: the force which does not produce any angular acceleration is known as static torque.
Example:
- Force applied on a closed-door is static torque because despite applying force on the door, the door is unable to rotate on its hinge.
- Static torque is applied by a boy who is pedaling a bicycle at a uniform speed as the bicycle is not accelerating.
Ques: The torque required to tighten a bolt attached to the main and rear frame of a mountain bike is 15N-m. Calculate the minimum length of the wrench that is required to attain the torque if a force 0f 40N can be applied to the wrench in any direction. (2 Marks)
Ans: The angle at maximum force is applied = 90o
T= F. r
Where, r = length of the wrench
r = TF
15N.m40N = 0.375 m
Ques: A weight of 100kg is applied at 3m to the left of a seesaw. To make the seesaw balanced, what distance should be maintained on the right side of the seesaw from the center? The mass of the body is given at 60kg. g = 10m/s2 (3 Marks)
Ans: Torque = rF sin\(\theta\)
As there is a downward projection of the weight inserted on the see saw, \(\theta\) = 0
Therefore, the weight applied by the torque = 3m. (100kg. 10 m/s2) = 3000 N
The weight inserted on the seesaw must be equal to 3000N to balance the seesaw.
3000N = r. (60kg.10 m/s2)
r = 5m
Ques: Two masses are attached to a meter stick. Mass 1 of 15kg weight is located at a distance of 10cm mark and mass 2 of 30 kg weight is located at 60cm mark. Determine the point where a string must be attached between the two masses so that the system is balanced. (3 Marks)
Ans: Torque = rF sin\(\theta\)
As force is perpendicular to distance, Torque = r F ( sine of 90o is 1 )
As force represented in this situation is gravity, F = mg
r1 (M1) = r2 (M2)
(x- 10)15 = (60-x) 30
X = 43
Ques: Two masses of 21 kg and 25.5 kg are carried by a seesaw at a distance of 4m and 2 m from the fulcrum respectively. How much weight should be placed at a distance of 9m from the fulcrum on the opposite side of the masses in order to balance the seesaw? (5 Marks)
Ans: To balance the seesaw, torque must be equal on both the side to create a rotational equilibrium
Torque (T) = Fd = mgd
T1 + T2 = T3
m1gd1 + m2gd2 = m3gd3
(21kg)g(4m) + (25.5kg)g(2m) = m3g (9m)
= 84kg.m+ 51kg.m = m3(9m)
135kg.m = m3(9m)
m3 = 15kg
Ques: A beam of 3m is balancing the weight with its fulcrum placed at the 1m mark from its left end. What will be the required force to be exerted on the left end if 50N force is applied on the right end. (5 Marks)
Ans: F1d1sin (\(\theta\)1) = F2d2 sin (\(\theta\)2)
Sin\(\theta\) = 1 as the force that are exerted are perpendicular to the beam.
F1d1 = F2d2
(50N) (2m) = x (1cm)
(50N)(2m)1m = 100N = x
The force on the left = 100N. the force must be not as strong as the force on the right.
Ques: A seesaw of 10m is being balanced by two students and is parallel to the ground. 5m is the length of each side of the seesaw. A student of 60kg is on the left side and standing at a distance of 3m away from the center whereas the student on the right side weighs 45kg. (5 Marks)
Ans: Torque = Fr sin\(\theta\)
Sin\(\theta\) = 1 as both the students will exert a downward force that is perpendicular to the seesaw.
F = mg = m (10 m/s2)
To keep the seesaw constant, the torque must be negligible or zero. There should be an equilibrium between the torque created by the lighter student on the right and the student on the left. By making the torques equal to each other, the distance can be calculated.
F1r1 = F2r2
(60kg)(10 m/s2)(3m) = (45kg)(10 m/s2) r2
r2 = 4m
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