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Moment Formula

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The moment is basically a force which is defined as the movement to rotate a body about a certain position. Let’s understand about the moment with the help of examples, If someone wants to close a window, they simply push off the handle with their finger and the window closes smoothly. Now try closing the window again but this time put the finger too close to the hinge and see if it’s too hard. Forces are used to make any body or object rotate. Hence the turning effect of force is known as the moment of force. There are many more examples of moments in our daily lives and these are,

  • Sight-seeing in the park
  • Open a can
  • Using a lever to lift a large load
  • A hammer is used to remove nails etc.

Moment of Force   

A moment of force is the movement that causes a body or object to rotate and is also known as torque. It is also defined as the product of force and perpendicular distance. The moment has both magnitude and direction.                  

Moment Formula

It is calculated by a formula,

M = F × d

Where M is the moment of force,

F is the applied force 

d is the distance from the fixed position.

This formula is applicable for both balanced and unbalanced forces. The S.I unit of the moment is the newton meter (Nm). Its dimensions are [ML2T-2] and its direction is given by the right-hand thumb rule.

Principle of Moment

It states that if a system is in equilibrium then the sum of its clockwise moments will be equal to the sum of its counterclockwise moments.

Clockwise moment = counter clockwise moment.

F1 × d1 = F2 × d2.

  • Clockwise Moment- A force causes an object or body to rotate in a clockwise direction. It is taken as positive.
  • Counterclockwise Moment – A force causes an object or body to turn in an anti-clockwise direction. It is taken as negative.

The term Equilibrium is defined as “it occurs when all the forces acting on a body are balanced”.

Applications of Principle of Moments 

  • We can find the mass of an object.
  • In simple machines.
  • It helps to account for how physical quantities are located and arranged.

Couple 

A couple is defined as a pair of two forces that are equal in magnitude but their direction are opposite to each other and the motion of lines do not coincide.

The formula of the couple:

τ = F × d.

S.I unit of couple = Newton-meter (Nm) and the dimensions are[ ML2T2].

Here the forces are equal and opposite so we get the result of force is zero and there is no linear acceleration.

Few Applications of the couple

  • Opening and closing the cap of the bottle.
  • Using the Key, unlock the locker.
  • Turning the screwdriver.
  • Helm wheel applied by the bus driver.

Momentum 

It is referred to as the property of the motion of an object. Momentum is defined as the product of the mass and velocity of an object. It is represented by the symbol ‘p’.

Formula of Momentum,

p = m × v

Where p = momentum of the body or an object 

m = mass of an object

v = velocity of an object.

S.I unit of momentum is Kg m/s.                           

Here are some problems based on the moment,

Sample Problems 

Question 1: A boy is sitting on one side of a see-saw 3m away from a point. If the weight of the boy is 20 N then find the moment.

Solution: 

Given that the boy’s weight caused an anticlockwise moment.                                      

Moment = Force × distance                                                                   

M = 20 × 3

M = 60Nm.

Question 2: The moment of force is 20 N about a fixed point is 2Nm. Calculate the distance of a point from the line of action of force.

Solution:

Given, Force = 20N and Moment = 2Nm.

Using the formula of moment which is M = F × d

2 = 20 × d 

d = 2/20

d = 0.1m.

Question 3: Find the force applied to a door causing a moment of 10Nm if the distance from the hinge axle to the point on the door is 2m where the force was applied.

 Solution:

Given, Moment (M) = 10Nm 

Distance (d) = 2m.

As we know  M = F × d

10 = F × 2

F = 10/2

F = 5N.

Question 4: A beam balance has its arms of length 100cm and 80cm. What weight kept on a pan of the longer arm will balance an object of weight 200gm kept on other pans?

Solution:

According to the principle of moments,

Clockwise moment = Anticlockwise moment

W × 100 = 200 × 80

W = (200 × 80)/100

W = 160gm.

Question 5: Two persons are sitting opposite sides on the see-saw, one person weighs 100N and is 2m from the pivot and the weight of other person is 200N. find where the person sits to balance the see-saw.

Solution:

According to the principle of moments,

Clockwise moment = Anticlockwise moment

100 × 2 = 200 × d

d = (100 × 2)/200

d = 1m.

Question 6: Is moment a scalar or a vector quantity? Explain

Solution:

By the formula of Moment, it is the product of force and distance of a fixed point or M = F × d.

As we know that force is a vector quantity. So Moment is also a vector quantity.

Question 7: Find the momentum of an object whose mass is 4Kg and moving with the velocity of 2m/s.

Solution: 

Given that Mass (m) = 4Kg and velocity (v) = 2m/s. According to the formula of momentum,

p = m × v

p = 4 × 2

p = 8 Kg m/s.



Last Updated : 04 Feb, 2024
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