Forces, Newton's laws and moments practice questions (A-Level Maths)

Sample questions

Key terms

The definitions and formulas A-Level Maths expects for forces, newton's laws and moments, typeset as they appear on the paper.

Newton's laws of motion

First: a body stays at rest or at constant velocity unless a resultant force acts. Second: resultant force equals mass times acceleration, applied in each direction separately. Third: forces between two bodies are equal and opposite.

$$F = ma$$

Weight and normal reaction

Weight acts vertically downward with magnitude $mg$. The normal reaction acts perpendicular to the surface; on a slope it is $mg\cos\theta$ for a particle in equilibrium perpendicular to the slope.

$$W = mg$$

Friction

Acts along the surface against the motion or the tendency to move, up to a maximum (limiting friction) proportional to the normal reaction. A body on the point of moving, or moving, has $F = \mu R$.

$$F \le \mu R, \qquad F_{\max} = \mu R$$

Connected particles

Bodies joined by a light inextensible string over a smooth pulley share the same acceleration and tension. Write Newton's second law for each body separately, then solve the simultaneous equations.

Resolving forces on an inclined plane

Resolve parallel and perpendicular to the slope: the component of weight down the slope is $mg\sin\theta$ and into the slope is $mg\cos\theta$. Include every force on the diagram before resolving.

$$mg\sin\theta - F = ma, \qquad R = mg\cos\theta$$

Equilibrium

A particle is in equilibrium when the resultant force is zero: the components in two perpendicular directions each sum to zero. For a rigid body, the moments about any point must also sum to zero.

Moments

The turning effect of a force: force times perpendicular distance from the pivot. For a rod in equilibrium take moments about a point that removes an unknown force, and treat the weight of a uniform rod as acting at its midpoint.

$$\text{moment} = F \times d, \qquad \sum \text{clockwise} = \sum \text{anticlockwise}$$

Tilting and the point of tipping

A rod resting on two supports is on the point of tilting about one support when the reaction at the other support is zero. Set that reaction to zero and take moments about the remaining support.

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Other A-Level Maths topics

• Proof, algebra and functions
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• Sequences and series
• Trigonometry
• Exponentials and logarithms
• Differentiation
• Integration
• Numerical methods and vectors
• Sampling and data presentation
• Probability and distributions
• Hypothesis testing
• Kinematics

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