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Moment of force refers to the tendency of forces to rotate a body about a specific point or axis. The point where the object rotates is called the axis of rotation.
- In our everyday life, we come across different kinds of forces.
- When we walk, when we pull a door, and even when we ride a bicycle, different kinds of force are experienced.
- By definition, force is the push or pull on an object with mass that causes it to change its velocity.
- Just as force causes linear acceleration, torque causes angular acceleration.
Key Terms: Torque, Force, SI units, Static and dynamic torque, Vector, Distance, Right-hand thumb rule.
Moment of Force(Torque)
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Torque or Moment of force is defined as the amount of force that is applied to an object which causes it to rotate on its axis. The point where the object rotates is called the axis of rotation. Mathematically, torque can be expressed as-
τ = r x F
Where
- τ = Torque
- r= radius from the axis
- F= Force applied on the object
Just as an external force is required for an object to accelerate in a linear motion, torque is required to cause angular acceleration for an object in a circular motion. Therefore, torque can also be defined as the rotational equivalent of linear force.
Torque is a vector quantity. The direction of the torque vector depends on the direction of force applied on its axis.
Also Read: Angular Momentum
Unit of Torque
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The S.I. unit of torque is Newton-metre (N-m).
In imperial units, foot-pound is used commonly.
The following is a table for the different units and symbols of torque-
| Symbol for torque | τ, M |
| SI unit | N.m |
| SI base unit | kg.m²/sec² |
| CGS unit | Dyne-centimetre (dyne.cm) |
| Dimensional formula | M¹L²/T² |
| Other units | Pound-force-feet, ft. lbs |
Read Also: Electric Motor
Types of Torque
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There are two types of torque, namely-
1. Static Torque:-
Static torque is the torque that does not produce angular acceleration.
Examples:
- When someone pushes a closed door, it is static torque since the door does not rotate despite applying force.
- A person pedaling a bicycle at constant speed is also an example of static torque because it does not cause acceleration.
2. Dynamic Torque:-
Dynamic torque is a torque that causes angular acceleration.
Example,
The drive shaft in a racing car that is accelerating from the starting line carries a dynamic torque since it must produce an angular acceleration of the wheels given that the car is accelerating along the track.
Calculations of Torque
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The magnitude of the torque is calculated by first determining the lever arm and then multiplying it by the applied force.
Now, we can conclude that the torque produced depends on the magnitude of the force and the perpendicular distance between the point at which torque is calculated and the point of applied force. So, mathematically torque is represented as:
τ = F.r. sinθ
where
- r is the length of the moment arm and
- θ is the angle between the force vector and the moment arm.
When, θ = 90° which means the angle between the force vector and the moment arm is a right angle,
Torque, τ = F. r sin (90°)
= F. r (since sin 90°=1)
Physics related Topics:
Direction of Torque
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The direction of the torque vector can be determined by using the Right-Hand Thumb Rule.
According to the Right-hand thumb rule, if you grip the imaginary axis of rotation of the rotational force so that your fingers point in the direction of the force, then the extended thumb points in the direction of the torque vector.
Application of Torque
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In every object experiencing torque, there is a pivot point. Some applications are provided below:
- Seesaws and Wrenches
- Gyroscopes
- A pendulum or a parachute is applying torque when swinging
- A person riding a bicycle
- Flag flying on a mast.
Check Important Link for: Fleming’s Left-Hand Rule
Things to Remember
- Moment of force or torque is defined as the amount of force that is applied to an object which causes it to rotate on its axis.
- Torque is a vector quantity.
- The direction of the torque vector depends on the direction of force applied on its axis.
- The S.I. unit of torque is Newton-metre (N-m).
- The direction of the torque vector can be determined by using the Right-Hand Thumb Rule.
Sample Questions
Ques. Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its center. Which of the two will acquire a greater angular speed after a given time? (3 marks)
Ans. The moment of inertia for the hollow cylinder = I1 = mr²
The moment of inertia for the solid sphere = I2 = 5/2mr²
For the hollow sphere, we have τ = I1α1
For the solid sphere, we have τ = I2α2
⇒ α2⁄α1= I1⁄ I2 = 5⁄2> 1
Thus,
α2>α1
ω(t)=ω0+αt
The angular velocity(ω) at a certain time will be greater for a solid sphere.
Ques. To maintain a rotor at a uniform angular speed of 200 rad s-1, an engine needs to transmit a torque of 180 Nm. What is the power required by the engine? (2 marks)
Ans. The angular speed of the rotor, ω = 200 rad/s
Torque required, τ = 180 Nm
The power of the rotor (P) is related to torque and angular speed by the relation:
P = τω
= 180 * 200 = 36 * 103
= 36 kW
Hence, the power required by the engine is 36 kW.
Ques. (a) A planet revolves around a massive star in a highly elliptical orbit whose angular momentum is constant over the entire orbit. Give a reason.
(b) What is the value of torque on the planet due to the gravitational force of the sun? (3 marks)
Ans. (a) A planet revolves around the star under the effect of gravitational force since the force is radial and does not contribute towards torque. Thus in the absence of an external torque angular momentum of the planet remains constant.
(b) The value of torque on the planet due to the gravitational force of the sun is Zero.
Ques. (a) Under what conditions, the torque due to an applied force is zero?
(b) If no external torque acts on a body, will its angular velocity remain conserved?
(c) A body is rotating at a steady rate. Is a torque acting on the body? (3 marks)
Ans. (a) We know that τ = rF sin θ. If θ = 0 or 180,
or
r = 0, then τ = 0, r = 0 means the applied force passes through the axis of rotation.
(b) No, the angular velocity will not remain conserved if no external torque acts on a body. It is the angular momentum that will be conserved.
(c) No, the torque is not acting on the body if it is rotating at a steady rate. Torque is required only for producing angular acceleration.
Ques. (a) Why cannot a single force balance the torque?
(b) Equal torques are applied on a cylinder and a sphere, both having the same mass and radius. The cylinder rotates about its axis and the sphere rotates about one of its diameters. Which one will acquire greater speed and why? (3 marks)
Ans. (a) The effect of torque is to produce angular acceleration and its effect is entirely different from that of the force which causes linear acceleration. Thus a single force cannot balance the torque.
(b)The speed of rotation acquired will depend upon the angular acceleration produced and is given by
α = τ ⁄ I
where,τ = Torque, I= moment of inertia,
As τ is the same in both cases, so
Thus, the sphere acquires greater speed than the cylinder as αs > αc.
Ques. On the application of constant torque, a wheel is turned from rest through an angle of 200 rads in 8s.
(a) What is its angular acceleration?
(b) If the same torque continues to act, what will be the angular velocity of the wheel after 16s from start? (3 marks)
Ans.:
Ques. Explain why friction is necessary to make the disc roll in the direction indicated. (3 marks)
(a) Give the direction of frictional force at B, and the sense of frictional torque, before perfect rolling begins.
(b) What is the force of friction after perfect rolling begins?
Ans. To roll a disc, we require torque, which can be provided only by a tangential force. The force of friction is the only tangential force needed to roll the disc in the indicated direction.
- The frictional force at B opposes the velocity of the point of contact B, which is to the left. The frictional force must be to the right. The frictional torque will be perpendicular to the plane of the disc and outwards.
- As frictional force at B decreases the velocity of the point of contact B with the surface. So, the perfect rolling begins only when the velocity of point B becomes zero. Also, the force of friction would become zero at this stage.
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