A push or pull on an object: a vector with a magnitude and a direction, measured in newtons (N).

State Newton's first law.

A particle remains at rest or moves with constant velocity unless acted on by a resultant force.

What does equilibrium mean?

The resultant force on the particle is zero, so it is at rest or moves with constant velocity.

Component of a force F at angle \theta along a direction?

F\cos\theta along the direction, F\sin\theta perpendicular to it.

Components of weight W on a plane inclined at \alpha?

W\sin\alpha down the plane and W\cos\alpha perpendicular to the plane.

What does constant velocity say about driving force and resistance?

They are equal in size and opposite in direction.

What changes if the resultant force is not zero?

The velocity changes (the particle accelerates).

What is the direction of the normal reaction?

Perpendicular to the surface, away from it.

Forces and Newton's first lawAQA A-Level Maths: Flashcards

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What is a force?

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What is a force?: A push or pull on an object: a vector with a magnitude and a direction, measured in newtons (N).
State Newton's first law.: A particle remains at rest or moves with constant velocity unless acted on by a resultant force.
What is the resultant force when velocity is constant?: Zero.
What does equilibrium mean?: The resultant force on the particle is zero, so it is at rest or moves with constant velocity.
How do you find the magnitude of $x\mathbf{i}+y\mathbf{j}$ ?: $\sqrt{x^2+y^2}$
Resultant of perpendicular forces $12$ N and $5$ N?: $13$ N
Component of a force $F$ at angle $\theta$ along a direction?: $F\cos\theta$ along the direction, $F\sin\theta$ perpendicular to it.
Components of weight $W$ on a plane inclined at $\alpha$ ?: $W\sin\alpha$ down the plane and $W\cos\alpha$ perpendicular to the plane.
What does constant velocity say about driving force and resistance?: They are equal in size and opposite in direction.
In equilibrium, what is $\mathbf{F}_1+\mathbf{F}_2+\mathbf{F}_3$ ?: $\mathbf{0}$
What changes if the resultant force is not zero?: The velocity changes (the particle accelerates).
What is the direction of the normal reaction?: Perpendicular to the surface, away from it.

Exam questions on Forces and Newton's first law

A particle is acted on by two horizontal forces: one of magnitude $12$ N, and one of magnitude $5$ N at right angles to it.
A third force $\mathbf{F}$ is now applied so that the particle moves with constant velocity. Find the magnitude and direction of $\mathbf{F}$ .2 marks
A crate of mass $40$ kg is pulled along level ground by a horizontal rope. The tension in the rope is $150$ N and the crate moves at constant velocity. Take $g=9.8$ m s⁻².
The tension is suddenly increased to $300$ N, with the resistance unchanged. Explain, using Newton's first law, why the crate no longer moves at constant velocity.2 marks
A particle is in equilibrium under the action of three forces $\mathbf{F}_1=(4\mathbf{i}+7\mathbf{j})$ N, $\mathbf{F}_2=(-9\mathbf{i}+2\mathbf{j})$ N and $\mathbf{F}_3$ , where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors.
Find $\mathbf{F}_3$ .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).