A force F acts at angle θ to a spanner of length l. What is its moment about the nut?

F l sin θ, because the perpendicular distance is l sin θ.

A pair of equal and opposite coplanar forces whose lines of action do not coincide.

What is the resultant force of a couple?

Zero. A couple gives a turning effect but no resultant force.

How do you calculate the moment of a couple?

One force multiplied by the perpendicular distance between the two lines of action.

State the principle of moments.

For a body in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point.

What two conditions give equilibrium of a body?

The resultant force is zero and the resultant moment about any point is zero.

Define centre of mass.

The point through which the whole weight of an object may be considered to act.

Why take moments about the point where an unknown force acts?

That force has zero moment about the point, so it does not appear in the equation.

What happens to the force at a support as a plank is about to tip about another support?

The force at the support it is lifting from falls to zero.

Moments, couples and centre of massAQA A-Level Physics: Flashcards

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Define the moment of a force about a point.

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Define the moment of a force about a point.: Force multiplied by the perpendicular distance from the point to the line of action of the force.
What is the unit of moment?: The newton metre (N m).
A force F acts at angle θ to a spanner of length l. What is its moment about the nut?: F l sin θ, because the perpendicular distance is l sin θ.
What is a couple?: A pair of equal and opposite coplanar forces whose lines of action do not coincide.
What is the resultant force of a couple?: Zero. A couple gives a turning effect but no resultant force.
How do you calculate the moment of a couple?: One force multiplied by the perpendicular distance between the two lines of action.
State the principle of moments.: For a body in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point.
What two conditions give equilibrium of a body?: The resultant force is zero and the resultant moment about any point is zero.
Define centre of mass.: The point through which the whole weight of an object may be considered to act.
Where is the centre of mass of a uniform regular solid?: At its geometric centre.
Why take moments about the point where an unknown force acts?: That force has zero moment about the point, so it does not appear in the equation.
What happens to the force at a support as a plank is about to tip about another support?: The force at the support it is lifting from falls to zero.

Exam questions on Moments, couples and centre of mass

A mechanic tightens a nut with a spanner. The force is applied at the end of the handle, at a distance of 0.35 m from the centre of the nut. The force has a magnitude of 120 N.
To loosen a stubborn nut a longer spanner is used, so that the same moment of 42 N m is produced by a force applied at right angles at a distance of 0.60 m from the nut. Calculate this force.2 marks
A driver turns a steering wheel of diameter 0.36 m by pulling down with one hand with a force of 8.0 N on one side of the rim and pushing up with the other hand with a force of 8.0 N on the opposite side. Both forces are tangential to the rim.
Explain why the wheel turns but is not pushed sideways by the driver's hands.2 marks
A uniform beam of length 4.0 m and weight 120 N is supported by a pivot. A child of weight 300 N sits on the beam at a point 0.50 m from its left end. The beam is horizontal.
The pivot is under the centre of the beam. A second child of weight 450 N sits on the other side of the pivot and the beam balances horizontally. Calculate the distance of the second child from the pivot.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).