Chapter 4: Forces – Vector and Moments

component of W down the slope=Wcos (90º- Ɵ)= W sin Ɵ
F=mgsinƟ
a=mgsinƟ/mg = gsinƟ

Moment of force

The moment of force is its turning affect about a fixed point.
The magnitude of the moment is given by:
Moment = force × perpendicular distance from force to the fixed point
moment=Fs
In the given figure, the force is not acting perpendicularly to the fixed point.
The perpendicular or the closest distance is scos Ɵ
The moment is given by moment=FscosƟ
We can also use value of s that would give:
moment=FcosƟs

Couples

A couple is a pair of equal forces acting in opposite directions. If a couple acts on an object it rotates in position.
The moment of couple is called torque. The torque is calculated as:
Torque = force × perpendicular distance between forces
torque=Fs
According to diagram,
torque=FscosƟ

 

Balance

When an object is balanced or at equilibrium:

the total moments acting clockwise=total moment acting anticlockwise

If a seesaw is left to balance then clockwise moment must be equal to anticlockwise moments.
Clockwise moment due to 3 and 4
moment=F3s3 + F4s4
Anticlockwise moment due to 1 and 2
moment= F1s1 + F2s2
So,
F3s3 + F4s4 = F1s1 + F2s2

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