AQA · A-Level · Mathematics

    Course version: 7357 · Version from Sept 2017

    R: Forces and Newton’s laws: Understand the concept of a force; understand and use Newton’s first law.

    A force is a push or pull that can change an object's motion or shape, measured in newtons and represented as a vector with magnitude and direction.

      Study notes

      From the checked teaching notes for this specification point.

      The idea

      A force is a push or pull that can change an object's motion or shape, measured in newtons and represented as a vector with magnitude and direction. Newton's first law states that a body remains at rest or moves with constant velocity unless acted on by a resultant force. This means zero resultant force gives zero acceleration, not necessarily zero velocity. For example, a book on a table has weight downwards and normal contact upwards; these cancel, so the book stays still. If the surface is frictionless and the book is sliding, it continues at constant speed. To use the law, identify all forces, resolve if needed, and check whether the resultant is zero. If it is, acceleration is zero; if not, motion changes. This underpins later work on equilibrium and dynamics.

      What earns the marks

      • Defines force as a vector quantity with magnitude and direction, measured in newtons.
      • States Newton's first law: a body remains at rest or moves with constant velocity unless acted on by a resultant force.
      • Explains that zero resultant force implies zero acceleration, not zero velocity.
      • Applies the law to identify equilibrium situations, such as a stationary object or one moving at constant speed.
      • Resolves forces in simple cases to show the resultant is zero or non-zero.
      • Distinguishes between balanced forces and the absence of forces.

      Common mistakes and how to put them right

      • Thinking that a moving object must have a resultant force acting on it.

        Put it right: Constant velocity means zero resultant force.

      • Confusing mass and force, using kilograms for force.

        Put it right: Force is measured in newtons; mass in kilograms.

      • Assuming that if an object is at rest, no forces act on it.

        Put it right: Forces may act but cancel to give zero resultant.

      Exam tips

      • Always draw a free-body diagram showing all forces acting on the object before applying Newton's first law.
      • State clearly that the resultant force is zero when velocity is constant, and link this to zero acceleration.
      • Use the wording 'constant velocity' rather than 'constant speed' when direction is fixed, as velocity includes direction.

      Try the lesson

      The start of the R: Forces and Newton’s laws: Understand the concept of a force; understand and use Newton’s first law. lesson, made from checked teaching notes for this specification point.

      Have a go first

      A book rests on a horizontal table and remains stationary. Which statement describes the forces acting on the book?

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