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Moments: turning forces

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Moments: turning forces

All: calculate the moment of a force about a point (torque) (C)

Most: apply principle of moments to simple balanced situations (B)

Some: employ principle of centre of mass in calculations (A)

Keywords:

Force

Moment

Couple

Torque

COM

Weight

Turning

All: calculate the moment of a force about a point (torque) (C)

Most: apply principle of moments to simple balanced situations (B)

Some: employ principle of centre of mass in calculations (A)

- Key Equation:
- Moment of a force = force x perpendicular distance
- moment = fd

Keywords:

Force

Moment

Couple

Torque

COM

Weight

Turning

All: calculate the moment of a force about a point (torque) (C)

Most: apply principle of moments to simple balanced situations (B)

Some: employ principle of centre of mass in calculations (A)

- What is the moment?
- Remember the unit!

Keywords:

Force

Moment

Couple

Torque

COM

Weight

Turning

All: calculate the moment of a force about a point (torque) (C)

Most: apply principle of moments to simple balanced situations (B)

Some: employ principle of centre of mass in calculations (A)

Note definition

The Principle of moments:

When an object is in equilibrium:

Sum of anti-clockwise moments about any point

Sum of clockwise moments about any point

=

clockwise moments – anticlockwise moments = zero (resultant force)

Centre of gravity is important for balancing

You have to keep the centre of gravity above the base if you want to balance.

Stability

I’m unstable.

The lower the centre of mass the better the stability. The tightrope walker’s pole helps.

August 19th 1859. French tightrope walker “Blondin” crosses the Niagara Falls with his manager on his back.

Slow, steady and stable

My head is big for my body compared to an adult’s head. That’s why I find it harder to balance.

Why are you not allowed to stand on the top of a double decker?

This lamp has a very heavy base. It will right itself if it is knocked over.

Producing an anti-capsize yacht.

This requires a turning force in the opposite direction to counteract it.

Centre of gravity is well behind the heel of the leading leg. This allows progressive loading of the leading leg.

Centre of gravity much closer to heel. This means that the loads on the heel, ankle, knee and pelvis rise sharply.

The centre of gravity of an aeroplane is affected by the way it is loaded. If the centre of gravity is in front of the centre of lift, the aircraft will want to nose down. The pilot will counterbalance this tendency by “trimming” the elevators to push the tail down. The opposite applies when the centre of gravity is behind the centre of lift.

Strange situations

Centre of gravity located outside body

Keywords:

Force

Moment

Couple

Torque

COM

Weight

Turning

All: calculate the moment of a force about a point (torque) (C)

Most: apply principle of moments to simple balanced situations (B)

Some: employ principle of centre of mass in calculations (A)

Demonstration: spoon and door

- Find centre of mass of a wooden spoon by balancing of finger
- Cut spoon through COM
- Weigh each piece

Keywords:

Force

Moment

Couple

Torque

COM

Weight

Turning

All: calculate the moment of a force about a point (torque) (C)

Most: apply principle of moments to simple balanced situations (B)

Some: employ principle of centre of mass in calculations (A)

Experiment 1: attaining equilibrium

- Place the metre rule so it has a pivot point at 50 cm
- Hang a 200g mass at 20 cm.
- Use a 100g mass to restore equilibrium
- Draw a diagram showing the arrangement and calculate the moments of each force acting

Keywords:

Force

Moment

Couple

Torque

COM

Weight

Turning

All: calculate the moment of a force about a point (torque) (C)

Most: apply principle of moments to simple balanced situations (B)

Some: employ principle of centre of mass in calculations (A)

0278

0278

(resourcefulphysics.org)

(resourcefulphysics.org)

Experiment 2

- Calculate the centre of mass (COM) for a volunteer
- Plank is placed at same height as scales
- Measure:
- change in weight, as shown on scales
- Weight of student
- The length of the plank

- Can you use this information to calculate where the COM is positioned? Theory here

HINT HERE

Keywords:

Force

Moment

Couple

Torque

COM

Weight

Turning

All: calculate the moment of a force about a point (torque) (C)

Most: apply principle of moments to simple balanced situations (B)

Some: employ principle of centre of mass in calculations (A)

0278

(resourcefulphysics.org)

Experiment 2 Theory

- Normal force = N, plank length = d, distance to COM = x, weight = W
Nd = Wx

Keywords:

Force

Moment

Couple

Torque

COM

Weight

Turning

All: calculate the moment of a force about a point (torque) (C)

Most: apply principle of moments to simple balanced situations (B)

Some: employ principle of centre of mass in calculations (A)

Experiment 3: calculate the weight of a metre ruler using moments

- Can assume the rule is uniform. How can we check?
- Place metre rule on a pivot at 15 cm.
- Locate an object of known mass on the shorter end until the ruler is balanced i.e. the moments are in equilibrium
- Draw a labelled diagram of the arrangement, noting the forces acting and their correct positions
- Apply the principle of moments to calculate the mass of the ruler

Keywords:

Force

Moment

Couple

Torque

COM

Weight

Turning

All: calculate the moment of a force about a point (torque) (C)

Most: apply principle of moments to simple balanced situations (B)

Some: employ principle of centre of mass in calculations (A)

Calculations

- Complete questions 1-4, page 98 in AQA book
- Complete questions 6-10 on page 108-109
- Home Learning: advanced warning! Complete all chapter 7 examination questions

Keywords:

Force

Moment

Couple

Torque

COM

Weight

Turning

All: calculate the moment of a force about a point (torque) (C)

Most: apply principle of moments to simple balanced situations (B)

Some: employ principle of centre of mass in calculations (A)

Experiment 1

- Place the metre rule so it has a pivot point at 50 cm
- Hang a 200g mass at 20 cm.
- Use a 100g mass to restore equilibrium
- Draw a diagram showing the arrangement and calculate the moments of each force