Gavin Howe
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, were first stated by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), originally published in 1687. Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will stay in motion with the same speed and in a straight line unless acted on by an unbalanced external force. The second law defines a force to be equal to the change in momentum (mass times velocity) per change in time. The third law states that for every action (force) in nature, there is an equal and opposite reaction. These laws have been used to explain and investigate many physical phenomena, including Kepler's laws of planetary motion, and remain among the most important physical laws today.
| Characteristics | Values |
|---|---|
| First Law of Motion | An object at rest remains at rest, and an object in motion remains in motion with the same speed and in a straight line unless acted on by an unbalanced force. |
| Second Law of Motion | The force acting on an object is equal to the product of its mass and acceleration. |
| Third Law of Motion | For every action, there is an equal and opposite reaction. |
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What You'll Learn
- Newton's first law of motion: an object at rest stays at rest, an object in motion stays in motion
- Newton's second law of motion: the relationship between force, mass, and acceleration
- Newton's third law of motion: for every action, there is an equal and opposite reaction
- Newton's law of universal gravitation
- Newton's cannonball thought experiment
Newton's first law of motion: an object at rest stays at rest, an object in motion stays in motion
Newton's first law of motion states that an object at rest will stay at rest, and an object in motion will stay in motion at a constant speed and in a straight line unless it is acted on by an unbalanced force. This tendency for objects to resist changes in their state of motion is called inertia.
Newton's first law can be traced back to Galileo Galilei, who first formulated the law of inertia for horizontal motion on Earth. Galileo deduced this law through his experiments with balls rolling down inclined planes. He aimed to explain why we do not sense the motion of the Earth spinning on its axis and orbiting the Sun. The principle of inertia provides the answer: as we are in motion with the Earth, our natural tendency is to retain that motion, so the Earth appears to us to be at rest.
Newton's first law can be applied to various scenarios, such as the motion of an aircraft when a pilot changes the throttle setting of an engine, a ball falling through the atmosphere, or a model rocket being launched. For example, consider a block on a smooth surface with no friction acting upon it. The only forces acting on the block are the force of gravity and the normal reaction by the surface, which cancel each other out, resulting in no net external force acting on the block. As the block remains at rest, it confirms Newton's first law of motion.
Newton's first law also has practical applications in our daily lives. For instance, wearing a seat belt while driving is an example of this law in action. In the event of an accident or sudden braking, the body will naturally tend to continue moving forward due to inertia, which could be fatal. Seat belts prevent this by stopping your body from moving forward, thus avoiding potential harm.
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Newton's second law of motion: the relationship between force, mass, and acceleration
Newton's second law of motion, unlike the first law, pertains to the behaviour of objects with unbalanced forces. This law is quantitative and is used to calculate what happens in situations involving a force.
Newton's second law states that the acceleration of an object depends on two variables: the net force acting on the object and the mass of the object. The acceleration of the body is directly proportional to the net force acting on the body and inversely proportional to the mass of the body. This means that as the force acting on an object is increased, the acceleration of the object also increases. Similarly, as the mass of an object is increased, its acceleration decreases.
The formula for Newton's second law of motion is F=ma, where F is force, m is mass, and a is acceleration. This means that for a constant mass, force equals mass times acceleration. Force is a product of mass and acceleration. When a force is applied to an object, it is referred to as thrust. The greater the thrust, the greater the acceleration. Acceleration is also dependent on the mass of the object; the lighter the object, the faster the acceleration.
Newton's second law can be observed in various situations. For example, when an object falls from a certain height, its acceleration increases due to the gravitational force. Similarly, in the case of a rocket, as it burns fuel, its mass decreases, resulting in increased acceleration over time.
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Newton's third law of motion: for every action, there is an equal and opposite reaction
Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that when two objects interact, they exert forces on each other that are equal in magnitude but opposite in direction. For example, if object A exerts a force on object B, object B will also exert a force on object A, but in the opposite direction. This is often summarised as "action equals reaction".
Newton's third law can be observed in various everyday situations. For instance, when a person walks, they push against the ground (the action), and the ground exerts an equal and opposite force (the reaction) that propels them forward. Similarly, when a swimmer pushes against the pool wall with their feet, they accelerate in the opposite direction of their push. In the case of a spinning ball, the air is deflected to one side (the action), causing the ball to move in the opposite direction (the reaction).
Newton's third law also applies to situations involving gravitational force. For example, when a ball is thrown against a wall, it exerts a force on the wall, and the wall exerts an equal force back on the ball, causing it to bounce off. Similarly, the Earth pulls objects downwards with gravity, but those objects also exert an equal force upwards on the Earth.
The fan and sail example is another classic illustration of Newton's third law. In this scenario, a fan is attached to a cart or sailboat and blows on its sail. According to the third law, the force of the air pushing in one direction should be cancelled out by the force exerted by the fan on the sail, resulting in the apparatus remaining stationary. However, if the sail redirects most of the airflow back towards the fan, the net force will cause the vessel to move.
Newton's third law holds significant importance in physics, as it underscores the fundamental concept that forces always occur in pairs. This law also led to the understanding that momentum is conserved during collisions between objects, even if the interaction is brief or the forces involved are not constant.
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Newton's law of universal gravitation
The equation for universal gravitation is: F = G(m1m2)/r^2, where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the centres of their masses, and G is the gravitational constant. The gravitational constant G is a universal constant that depends on the system of units used. Its value is extremely difficult to measure accurately, but it was first determined by Henry Cavendish in 1798 through a clever apparatus that measured the gravitational force between two pairs of masses.
While Newton's law of universal gravitation has been superseded by Albert Einstein's theory of general relativity, it still continues to be used as an excellent approximation of the effects of gravity in most applications. Relativity is required only when dealing with very strong gravitational fields or when extreme accuracy is needed.
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Newton's cannonball thought experiment
Newton's three laws of motion describe the relationship between the motion of an object and the forces acting on it. Newton's cannonball, also known as Newton's Cannon, is a thought experiment created by Isaac Newton in 1687. In this experiment, Newton imagined firing a cannonball parallel to the Earth's surface from the top of a very high mountain. The outcome would depend on the velocity of the cannonball—it could strike the ground at some distance from the mountain top, go into orbit around the Earth, or fly off into space.
Newton's cannonball experiment interpolates between projectile motion and uniform circular motion. If a cannonball is dropped from rest off the edge of a tall cliff, it will hit the ground in the same amount of time as if it were lobbed weakly off the edge, because the force of gravity only affects the cannonball's momentum in the downward direction. The effect is not diminished by horizontal movement. However, if the cannonball is launched with a greater initial horizontal velocity, it will travel farther before hitting the ground, but it will still take the same amount of time.
The horizontal velocity of the cannonball will remain constant due to Newton's First Law, also known as the Law of Inertia, which states that an object will remain at rest or in uniform motion in a straight line unless compelled to change by an external force. The vertical velocity of the cannonball, however, will be affected by Earth's gravity and will increase at the rate of acceleration due to gravity.
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Frequently asked questions
Newton's Laws of Motion are three physical laws that describe the relationship between an object's motion and the forces acting on it.
Newton's First Law states that an object at rest will stay at rest, and an object in motion will stay in motion unless acted on by a net external force. This can be proven through various everyday examples, such as the motion of a ball on a slanted surface or a book on a table.
Newton's Second Law defines force as equal to the change in momentum (mass times velocity) per change in time. This can be proven mathematically using the equation: F = (m1 x V1 - m0 x V0) / (t1 - t0).
More elaborate proofs and examples can be provided for each of Newton's Laws, but these answers provide a basic understanding of how they can be proven.
