A-Level Moments Practice Questions

Free A-Level Moments practice questions with full step-by-step worked solutions. Covers moment, turning-effect, weight, resultant. Practise exam-style problems and check your method.

momentturning-effectweightresultantequilibriummoments
A-Level70 questionsStep-by-step solutions
Question 1
2 markseasy
A force of 10 N10\,\text{N} acts at a perpendicular distance of 2 m2\,\text{m} from a pivot. Find the magnitude of the moment about the pivot.
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Worked solution

  1. Recall the moment formula

    M=FdM=Fd

    The moment of a force about a point equals the force times the perpendicular distance.

  2. Substitute the force and distance

    M=10×2M=10\times 2

    Insert the given values.

  3. State the moment

    M=20 N mM=20\,\text{N m}

    This is the required moment.

Answer
M=20 N mM=20\,\text{N m}
Question 2
2 markseasy
A uniform rod of length LL is placed horizontally. At what distance from one end does its weight act?
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Worked solution

  1. Recall the uniform rod model

    mass distributed evenly\text{mass distributed evenly}

    A uniform rod has equal mass per unit length.

  2. Identify the balance point

    geometric centre\text{geometric centre}

    The weight acts at the midpoint.

  3. Select the correct position

    L2\dfrac{L}{2}

    The weight acts at half the length from either end.

Answer
L2\dfrac{L}{2}
Question 3
3 marksintermediate
A uniform beam rests horizontally on two supports and is in equilibrium. Which pair of conditions must hold?
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Worked solution

  1. Recall beam equilibrium

    two conditions\text{two conditions}

    A beam in equilibrium must satisfy both force and moment conditions.

  2. List the conditions

    ΣF=0, ΣM=0\Sigma F=0,\ \Sigma M=0

    Zero resultant force and zero resultant moment.

  3. Recall the modelling assumptions

    rigid body, coplanar forces\text{rigid body, coplanar forces}

    Standard moment problems treat the body as rigid with forces in one plane.

  4. Note the pivot point

    moments are taken about the stated pivot\text{moments are taken about the stated pivot}

    The pivot is the reference point for all distances.

  5. Distinguish force and moment

    force in N, moment in N m\text{force in N, moment in N m}

    A moment is not the same as a force.

  6. Select the correct pair

    ΣF=0, ΣM=0\Sigma F=0,\ \Sigma M=0

    Both conditions are required.

Answer
ΣF=0, ΣM=0\Sigma F=0,\ \Sigma M=0
Question 4
5 markshard
A force acts along a rod, in the same direction as the rod, at the end of the rod. What is the moment of this force about the other end of the rod?
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Worked solution

  1. Recall the moment formula

    M=Fdsin⁡θM=Fd\sin\theta

    Only the perpendicular component of distance contributes.

  2. Consider a force parallel to the rod through its end

    θ=0∘⇒M=0\theta=0^\circ\Rightarrow M=0

    When the force acts along the rod, the perpendicular distance is zero.

  3. Recall the modelling assumptions

    rigid body, coplanar forces\text{rigid body, coplanar forces}

    Standard moment problems treat the body as rigid with forces in one plane.

  4. Note the pivot point

    moments are taken about the stated pivot\text{moments are taken about the stated pivot}

    The pivot is the reference point for all distances.

  5. Distinguish force and moment

    force in N, moment in N m\text{force in N, moment in N m}

    A moment is not the same as a force.

  6. Check the units

    N m = N×m\text{N m = N}\times\text{m}

    Moment units are newton metres.

  7. State the equilibrium conditions

    ΣF=0, ΣM=0\Sigma F=0,\ \Sigma M=0

    Complete equilibrium needs both conditions.

  8. Recall the sign convention

    anticlockwise positive\text{anticlockwise positive}

    A consistent sign convention is needed to add moments.

  9. Identify the lever arm

    d is perpendicular to the forced\ \text{is perpendicular to the force}

    Only the perpendicular distance counts.

  10. Select the correct moment

    M=0M=0

    A force parallel to the lever arm produces no moment about that point.

Answer
M=0M=0
Question 5
8 markschallenging
Two particles of masses m1m_1 and m2m_2 lie on a straight line at positions x1x_1 and x2x_2. Which expression gives the xx-coordinate of their centre of mass?
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Worked solution

  1. Recall the centre of mass formula

    xˉ=m1x1+m2x2m1+m2\bar{x}=\dfrac{m_1x_1+m_2x_2}{m_1+m_2}

    The centre of mass is a weighted average of positions.

  2. Note the weighting

    heavier mass has more influence\text{heavier mass has more influence}

    Larger masses pull the centre of mass closer.

  3. Recall the modelling assumptions

    rigid body, coplanar forces\text{rigid body, coplanar forces}

    Standard moment problems treat the body as rigid with forces in one plane.

  4. Note the pivot point

    moments are taken about the stated pivot\text{moments are taken about the stated pivot}

    The pivot is the reference point for all distances.

  5. Distinguish force and moment

    force in N, moment in N m\text{force in N, moment in N m}

    A moment is not the same as a force.

  6. Check the units

    N m = N×m\text{N m = N}\times\text{m}

    Moment units are newton metres.

  7. State the equilibrium conditions

    ΣF=0, ΣM=0\Sigma F=0,\ \Sigma M=0

    Complete equilibrium needs both conditions.

  8. Recall the sign convention

    anticlockwise positive\text{anticlockwise positive}

    A consistent sign convention is needed to add moments.

  9. Identify the lever arm

    d is perpendicular to the forced\ \text{is perpendicular to the force}

    Only the perpendicular distance counts.

  10. Summarise the key idea

    turning effect =Fd\text{turning effect }=Fd

    The moment measures the turning effect of a force.

  11. Apply to a uniform rod

    W acts at the centreW\ \text{acts at the centre}

    A uniform rod's weight acts at its midpoint.

  12. Relate to centre of mass

    xˉ=∑mixi∑mi\bar{x}=\dfrac{\sum m_ix_i}{\sum m_i}

    The centre of mass is the weighted average of positions.

  13. Consider tilting

    R=0 at one supportR=0\ \text{at one support}

    Tilting begins when a support reaction becomes zero.

  14. Verify the logic

    check against the definition\text{check against the definition}

    The correct answer follows from the definition.

  15. Select the correct formula

    xˉ=m1x1+m2x2m1+m2\bar{x}=\dfrac{m_1x_1+m_2x_2}{m_1+m_2}

    This is the formula for two particles on a line.

Answer
xˉ=m1x1+m2x2m1+m2\bar{x}=\dfrac{m_1x_1+m_2x_2}{m_1+m_2}

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