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What is Newton's second law of motion?

Class 11 PhysicsNCERT chapter: Laws of Motionइसे हिंदी में पढ़ें

Exam-ready answer

Newton's second law states that the rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts. Mathematically F = dp/dt. For a body of constant mass, F = ma. The SI unit of force is the newton (1 N = 1 kg m s⁻²).

Explanation

Momentum (p) of a body is the product of its mass and velocity, p = mv. It is a vector with the direction of velocity. Everyday experience shows that a larger force is needed to stop a heavy truck than a light cart moving at the same speed, and a fast cricket ball hurts more than a slow one. The effect of a force is therefore best described through the change it produces in momentum.

The second law says F ∝ Δp/Δt. Choosing units so that the constant of proportionality is 1, F = dp/dt. If the mass m stays constant, dp/dt = m dv/dt = ma. One newton is the force that gives a mass of 1 kg an acceleration of 1 m s⁻². The law is a vector equation, so it holds separately for each component: Fx = max, Fy = may, Fz = maz.

Important features: F is the net external force on the body; internal forces are not included. A force along one direction changes only the velocity component along that direction. If F = 0, then a = 0, which agrees with the first law. A fielder pulling his hands back while catching a ball increases the time of contact, so the force on his hands is smaller.

Points to remember

  1. Statement: rate of change of momentum is directly proportional to the applied force and is in the direction of the force.
  2. Formula: F = dp/dt; for constant mass, F = ma.
  3. Momentum p = mv; SI unit kg m s⁻¹; it is a vector.
  4. SI unit of force: newton (N); 1 N = 1 kg m s⁻².
  5. F is the net external force; the law is a vector equation and applies to each component separately.

Exam tip

Write the statement in full, then F = dp/dt and the step d(mv)/dt = m dv/dt = ma for constant mass. Finish with the SI unit and the definition of 1 newton.

Questions students also ask

How does a cricketer reduce the force of a fast ball while catching it?
He moves his hands backward with the ball. This increases the time taken to bring the ball to rest. Since force equals change in momentum divided by time, a longer time means a smaller force on the hands, so the catch hurts less.
Is the first law contained in the second law?
Yes. If the net external force is zero, F = ma gives a = 0. The body then stays at rest or keeps moving with uniform velocity, which is exactly what the first law states.
What is impulse?
Impulse is the product of force and the time for which it acts, and it equals the change in momentum of the body. It is useful when a large force acts for a very short time, such as a bat hitting a ball. Its SI unit is N s, the same as kg m s⁻¹.

Chapter labels help you find the topic in your textbook. Check your own edition: chapter names and order can change. These are Know.it explanations, not official NCERT solutions.