AQA · A-Level · Physics

    Course version: 7408 · Version from Sept 2016

    Expressions for moment of inertia will be given where necessary.

    Full specification wording

    Concept of moment of inertia (A-level only): Expressions for moment of inertia will be given where necessary.

    Moment of inertia, symbol I, measures how a body's mass is distributed about a chosen axis and therefore how strongly it resists angular acceleration.

    Checked against the AQA 7408 specification (opens in a new tab) on .

    • Point 2 of 2
    • 4 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    Moment of inertia, symbol I, measures how a body's mass is distributed about a chosen axis and therefore how strongly it resists angular acceleration. For a point mass, I = mr², where m is mass and r is perpendicular distance from the axis. Extended bodies have expressions such as I = ½mr² for a uniform solid disc about its central axis, I = mr² for a thin ring, and I = (2/5)mr² for a uniform solid sphere about a diameter. You are not expected to derive these standard results; where a question needs one, it will be supplied. Your task is to select the correct expression, substitute values in SI units, and combine it with τ = Iα or rotational kinetic energy ½Iω².

    For example: A 2.0 kg solid disc of radius 0.10 m has I = ½ × 2.0 × (0.10)² = 0.010 kg m².

    What earns the marks

    • State that moment of inertia depends on both the total mass and how that mass is distributed relative to the axis of rotation.
    • Use a supplied expression correctly, substituting mass in kg and distance in m so that I is quoted in kg m².
    • Recognise that the same body has different moments of inertia about different axes, so the axis must be identified before choosing an expression.
    • Combine a given I with τ = Iα to find angular acceleration, or with ½Iω² to find rotational kinetic energy.
    • Check that the expression supplied matches the shape and axis described, for example a solid disc about its central axis rather than about a rim.

    Common mistakes and how to put them right

    • Using the wrong radius.

      Put it right: Halve any diameter before squaring.

    • Forgetting to square the distance.

      Put it right: Apply the squared term before multiplying by mass.

    • Mixing units: the error is leaving mass in g or radius in cm; the correction is to convert to kg and m so the answer is in kg m².

    Exam tips

    • Read the axis description carefully; a disc about its centre and a disc about its rim have different expressions.
    • Write the supplied expression first, then substitute numbers, so the examiner can follow your method.
    • Carry units through the calculation and give the final answer in kg m² to an appropriate number of significant figures.

    Try the lesson

    The start of the Concept of moment of inertia (A-level only): Expressions for moment of inertia will be given where necessary. lesson, made from checked teaching notes for this specification point.

    Have a go first

    A solid disc of mass 4.0 kg and radius 0.50 m rotates about its central axis. Using the given expression I = ½mr², what is the moment of inertia of the disc?

    Listen

    Moment of inertia, symbol I, measures how a body's mass is distributed about a chosen axis and therefore how strongly it resists angular acceleration. For a point mass, I = mr², where m is mass and r is perpendicular distance from the axis. Extended bodies have expressions such as I = ½mr² for a uniform solid disc about its central axis, I = mr² for a thin ring, and I = (2/5)mr² for a uniform solid sphere about a diameter. You are not expected to derive these standard results; where a question needs one, it will be supplied. Your task is to select the correct expression, substitute values in SI units, and combine it with τ = Iα or rotational kinetic energy ½Iω². For example, a 2.0 kg solid disc of radius 0.10 m has I = ½ × 2.0 × (0.10)² = 0.010 kg m². A strong answer earns marks for these points. State that moment of inertia depends on both the total mass and how that mass is distributed relative to the axis of rotation. Use a supplied expression correctly, substituting mass in kg and distance in m so that I is quoted in kg m². Recognise that the same body has different moments of inertia about different axes, so the axis must be identified before choosing an expression. Combine a given I with τ = Iα to find angular acceleration, or with ½Iω² to find rotational kinetic energy. A common slip: Using the wrong radius: the error is substituting diameter for r. Instead, halve any diameter before squaring. Exam tip: Read the axis description carefully; a disc about its centre and a disc about its rim have different expressions.

    See it

    A top-down flowchart with seven nodes. The first node says identify the shape and the axis, and points to select the supplied expression for I. That points to convert mass to kg and distance to m, which points to substitute values, squaring the distance, which points to quote I in kg m². From that node two branches lead out: one to combine with τ = Iα and one to combine with ½Iω².
    The sequence of steps for choosing a supplied moment of inertia expression, substituting values to find I in kg m², and then applying it in a rotational dynamics or energy equation.

    Key words

    Say what each word means before you turn the card.

    Moment of inertia

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    Mass distribution

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    Angular acceleration

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    Use of standard results

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    See every definition
    Moment of inertia
    Measures how a body's mass is distributed about a chosen axis and therefore how strongly it resists angular acceleration.
    Mass distribution
    How a body's mass is spread about a chosen axis, which moment of inertia measures.
    Angular acceleration
    The quantity that moment of inertia measures how strongly a body resists.
    Use of standard results
    Standard expressions are not derived; where a question needs one, it will be supplied, and the correct expression must be selected.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A top-down flowchart with seven nodes. The first node says identify the shape and the axis, and points to select the supplied expression for I. That points to convert mass to kg and distance to m, which points to substitute values, squaring the distance, which points to quote I in kg m². From that node two branches lead out: one to combine with τ = Iα and one to combine with ½Iω².

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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