Moments

1. Torque

1.1. it is the force applied a distance away from the pivot point or axis rotation.

1.2. Force (N) x Perpendicular distance (m) = Torque (Nm)

1.3. distance must be perpendicular to force

1.4. it is applied somewhere other than the CoM

1.5. when an object rotates CLOCKWISE, the value of torque is negative.

1.6. when an object rotates ANTI-CLOCKWISE, the value of torque is positive.

1.7. distance vector and force vector are perpendicular to each other

2. Note: work done does not equal to torque

2.1. work: distance vector and force vector are parallel to each other and in the same direction

2.2. torque: distance vector and force vector are perpendicular to each other

3. Equilibrium

3.1. Neutral

3.1.1. the frustrum will roll about but will not topple

3.1.2. its centre of gravity remains at the same height when it is displaced

3.1.3. the body will stay in any position to which it has been displaced

3.2. Conditions for stability

3.2.1. lowering its centre of gravity

3.2.2. increasing the area of its base

3.3. Unstable

3.3.1. the frustrum will topple slightly upon the slightest tilting

3.3.2. its centre of gravity is lowered when it is displaced

3.3.3. its weight has a moment about its pivot which causes it to topple

3.4. Stable

3.4.1. the frustrum can be tilted at quite a big angle without toppling over

3.4.2. its centre of gravity increases when it is displaced

3.4.3. its weight has a moment about the pivot which causes it to return back to its original position

4. sum of clockwise moments about a point = sum of anticlockwise moments about the same point

5. Centre of Mass

5.1. it is a point, not necessarily in the object

5.2. entire mass of object exists here

5.3. it has a uniform distribution if it is made out of the same material and is of uniform density

5.4. one-dimensional geometric centre

5.5. when force is applied directly on the CoM, the object will move in the direction of that force with the appropriate acceleration

5.6. if a force is applied some place else away from the CoM, the object will rotate around the CoM when it is free and not fixed to any other point (spinning around the CoM)

5.7. therefore, the point of which the object rotates around is known as the CoM

5.8. EXAMPLE: High jumpers. Less forces are required when they arch their backs over the bar. Their CoM is below the bar, allowing the athlete to successfully jump over the bar exerting minimum force