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Dynamics: Class 9 Physics
Force and its effects, Newton's three laws of motion, mass and weight, momentum and its conservation, friction, and motion in a circle with centripetal force.
Key points
Dynamics is the study of motion together with the forces that cause it. A force is a push or a pull. It can start or stop a motion, change speed or direction, or change the shape of a body. Force is a vector. Its SI unit is the newton (N). One newton is the force that gives a mass of 1 kg an acceleration of 1 m/s².
Newton's first law (law of inertia): a body stays at rest, or keeps moving in a straight line at constant speed, unless an unbalanced force acts on it. Inertia is the property of a body to resist any change in its state of rest or motion. Mass is the measure of inertia: a heavy truck is harder to start and harder to stop than a bicycle.
Everyday examples of inertia are:
- Passengers lean forward when a bus brakes suddenly, because their bodies tend to keep moving.
- Passengers fall backwards when a bus starts suddenly, because their bodies tend to stay at rest.
- Dust flies off a carpet when it is beaten, because the dust stays at rest as the carpet moves.
Momentum is the product of mass and velocity: p = mv. It is a vector in the direction of the velocity. Its SI unit is kg m/s, which is the same as N s. A heavy body moving fast has large momentum. A small bullet can have large momentum because of its high speed.
Newton's second law: the acceleration of a body is directly proportional to the net force and inversely proportional to its mass, in the direction of the force. This gives F = ma. Equivalently, the net force equals the rate of change of momentum: F = (mvf − mvi)/t. Doubling the force doubles the acceleration. Doubling the mass halves it.
Mass is the quantity of matter in a body. It is a scalar, measured in kg, and does not change from place to place. Weight is the force with which the Earth pulls a body, so W = mg. It is a vector pointing towards the centre of the Earth and is measured in newtons. Weight changes with place: on the Moon, where g is about one sixth of that on Earth, a body weighs one sixth as much but has the same mass.
Newton's third law: to every action there is an equal and opposite reaction. The two forces act on different bodies, so they never cancel each other. A rocket pushes gas backwards and the gas pushes the rocket forwards. A swimmer pushes the water back and the water pushes the swimmer forward. A gun recoils when it fires a bullet.
The law of conservation of momentum: when no external force acts on a system of bodies, the total momentum before a collision equals the total momentum after it. For two bodies, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. It follows from the second and third laws. It explains the recoil of a gun and the motion of rockets.
Friction is the force that opposes the relative motion, or the tendency of motion, between two surfaces in contact. It acts along the surfaces. Static friction acts when the body is at rest and rises up to a maximum value called limiting friction. Sliding friction acts on a moving body and is smaller than limiting friction. Rolling friction is smaller still. The friction force is f = μN, where N is the normal reaction and μ is the coefficient of friction, which has no unit.
Friction has advantages and disadvantages:
- Useful: we can walk, brakes can stop vehicles, and nails and screws hold in place.
- Harmful: it wears out machine parts, produces heat and wastes energy.
- Reduced by lubricants, polishing, ball bearings and streamlined shapes.
A body moving in a circle at constant speed has a velocity that keeps changing direction, so it is accelerating towards the centre. The force that provides this is the centripetal force. Its size is Fc = mv²/r, directed towards the centre. If the string breaks, the body flies off along the tangent. For a satellite, gravity supplies the centripetal force.
Study tip: For numericals, first draw the situation and mark the forces or the before and after states. In momentum questions, always write total momentum before and after as separate lines. For long questions on laws, give the statement, then a daily-life example, then the formula.
Definitions and flashcards
Say the meaning first, then open the card to check.
Force
A push or pull that can change the state of motion or shape of a body.
Inertia
The tendency of a body to resist a change in its state of rest or of uniform motion.
Momentum
Product of mass and velocity of a body, in kg m/s.
Weight
The force of gravity on a body, equal to mg.
Newton
The force that gives 1 kg an acceleration of 1 m/s².
Friction
A force opposing relative motion between surfaces in contact.
Limiting friction
The maximum value of static friction, just before sliding begins.
Centripetal force
The inward force that keeps a body moving in a circle.
Coefficient of friction
The ratio of friction force to normal reaction, μ = f/N.
Formula sheet
| Name | Formula | What it means |
|---|---|---|
| Second law | F = ma | Net force equals mass times acceleration |
| Momentum | p = mv | Mass times velocity |
| Force and momentum | F = (mvf − mvi)/t | Rate of change of momentum |
| Weight | W = mg | Force of gravity on mass m |
| Conservation of momentum | m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ | Total momentum before equals after |
| Friction | f = μN | Friction force from normal reaction |
| Centripetal force | Fc = mv²/r | Inward force for circular motion |
Short questions with model answers
These are the kind of questions asked for 2, 3 and 5 marks. Try each one before opening the answer.
State Newton's first law of motion. (2 marks)
A body at rest stays at rest, and a body in motion keeps moving in a straight line with constant speed, unless an unbalanced force acts on it.
Why is mass called a measure of inertia? (2 marks)
A body with more mass needs a larger force to change its motion by the same amount. So the greater the mass, the greater the resistance to change. Hence mass measures inertia.
Differentiate between mass and weight. (3 marks)
Mass is the amount of matter in a body. It is a scalar, measured in kg, and is the same everywhere. Weight is the force of gravity on the body. It is a vector, measured in newtons, and equals mg. It changes with the value of g, so it is less on the Moon than on Earth.
Why do action and reaction not cancel each other? (3 marks)
Action and reaction are equal in size and opposite in direction. But they act on two different bodies. Forces cancel only when they act on the same body. Hence each body feels only one of the two forces, and both can produce motion.
State and explain the law of conservation of momentum. (5 marks)
When no external force acts on a system, its total momentum stays constant. Take two bodies of masses m₁ and m₂ moving with velocities u₁ and u₂ that collide. After the collision their velocities are v₁ and v₂. Then m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. During the collision each body exerts an equal and opposite force on the other for the same time. So the momentum lost by one equals the momentum gained by the other, and the total is unchanged. A gun and bullet start at rest with zero total momentum. After firing the bullet moves forward and the gun recoils backwards with equal and opposite momentum.
Write the advantages and disadvantages of friction and name ways to reduce it. (5 marks)
Advantages: friction lets us walk without slipping, makes brakes and tyres grip the road, and holds nails and screws in place. Disadvantages: it wears out the moving parts of machines, produces unwanted heat and wastes energy. Friction can be reduced by oiling or greasing the surfaces, by polishing them, by using ball bearings or rollers that replace sliding with rolling, and by giving vehicles a streamlined shape against air.
Numericals with worked steps
A force of 24 N acts on a body of mass 6 kg. Find its acceleration. How much velocity does it gain in 5 s starting from rest?
- F = 24 N, m = 6 kg
- a = F/m = 24/6 = 4 m/s²
- vf = vi + at = 0 + 4 × 5 = 20 m/s
Answer: a = 4 m/s², velocity gained 20 m/s
A 2 kg trolley moving at 3 m/s collides with a 1 kg trolley at rest. They stick together. Find their common velocity.
- m₁ = 2 kg, u₁ = 3 m/s, m₂ = 1 kg, u₂ = 0
- Momentum before = 2 × 3 + 1 × 0 = 6 kg m/s
- After: (2 + 1) v = 3v
- 3v = 6, so v = 2 m/s
Answer: 2 m/s in the original direction
A 0.05 kg bullet leaves a 4 kg gun at 200 m/s. Find the recoil velocity of the gun.
- Total momentum before firing = 0
- 0 = 0.05 × 200 + 4 × v
- 10 + 4v = 0, so v = −10/4 = −2.5 m/s
Answer: 2.5 m/s, opposite to the bullet
A box of mass 20 kg rests on a floor. The coefficient of friction is 0.3. Take g = 10 m/s². Find the force needed to start sliding it.
- Normal reaction N = mg = 20 × 10 = 200 N
- f = μN = 0.3 × 200 = 60 N
- A pull just greater than the limiting friction starts the motion
Answer: 60 N
A 0.5 kg stone is whirled in a circle of radius 2 m at 4 m/s. Find the centripetal force.
- Fc = mv²/r
- = 0.5 × 4² / 2 = 0.5 × 16 / 2
- = 8/2 = 4 N
Answer: 4 N towards the centre
Common mistakes
- Saying action and reaction cancel. They act on different bodies, so they cannot cancel.
- Writing weight in kg. Weight is a force and is measured in newtons.
- Believing a force is needed to keep a body moving at constant velocity. Without friction, no force is needed.
- Forgetting the sign of velocity in momentum problems, especially for recoil, where the signs are opposite.
- Treating the centripetal force as an extra force. It is the name for the net inward force, such as tension or gravity.