Introduction to Dynamics

While kinematics describes motion, dynamics explains the cause of motion. The fundamental concept in dynamics is force. An external force is required to change the velocity of a body.

Newton's First Law of Motion

Newton built upon Galileo's ideas and formulated his First Law, also known as the Law of Inertia:

"Every body continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise."

This law defines both force and inertia.

  • Inertia: It is the inherent property of a body to resist any change in its state of rest or uniform motion. Mass is a quantitative measure of a body's inertia. The more mass an object has, the greater its inertia.
  • Force: The First Law defines force as the external agent that causes a change in the state of motion of a body. If the net external force on a body is zero, its acceleration is zero.

Key Concepts:

  • If no net force acts on a body, its velocity remains constant.
  • If a body is at rest, it remains at rest until a force acts.
  • If a body is moving uniformly, it continues to move uniformly in the same direction.

Types of Inertia:

  1. Inertia of Rest – A body at rest remains at rest.

  2. Inertia of Motion – A body in motion remains in motion.

  3. Inertia of Direction – A body resists change in direction of motion.

    Illustration of Newton’s First Law with examples

    Examples:

  • Passenger jerks forward when a bus stops suddenly (inertia of motion)
  • Dust comes off a mat when beaten (inertia of rest)
  • Water spills out of a bucket in circular motion (inertia of direction)

Inertial Frames of Reference

A frame of reference in which Newton's first law is valid is called an inertial frame of reference. Any frame moving at a constant velocity with respect to an inertial frame is also an inertial frame. A frame that is accelerating (like a car turning a corner or a freely falling elevator) is a non-inertial frame.

Example:

An astronaut accidentally gets separated from his small spaceship, which is accelerating in interstellar space at a constant rate of 100 m/s2100\ m/s^2. What is the acceleration of the astronaut the instant after he is outside the spaceship? (Assume no nearby stars exert gravitational force).

Solution:

  1. Identify Forces: Before separation, the spaceship exerts a contact force on the astronaut, causing him to accelerate at 100 m/s2100\ m/s^2. The instant after he is outside, this contact force becomes zero.
  2. Apply Newton's First Law: The problem states to assume there are no other external forces (like gravity from stars). Therefore, the net external force on the astronaut is zero.
  3. Conclusion: According to Newton's First Law, if the net external force on a body is zero, its acceleration must also be zero. The astronaut will continue to move with the constant velocity he had at the instant of separation, but his acceleration will be zero.