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In dynamics, a reference frame, also known as a frame of reference, is a set of graded lines symbolically tied to a body that characterises the position of points relative to the body.
Coordinate systems are reference frames used in dynamics, with axes (lines) originating from a point known as the origin. Two integers can be used to indicate the position of a point travelling parallel to a plane (plane motion):
- the distances between a point and two lines on the plane that are at right angles to one another (rectangular coordinates).
- the length of a line with one end fixed at the origin and the other end at the moving point; also, the angle the line forms with a fixed axis (polar coordinates).
Frame of Reference
For example, consider a car moving at 100 km/hr. While calculating the car’s speed, we completely ignore that the earth’s surface is rotating at the equator at a speed of 1670 km/hr, and the velocity of the earth’s orbit around the sun is 30 km/s. If we calculate the car’s motion, we see the car moving at tremendous speed with the motion of the earth and sun added to it. Here is where the frame of reference comes into the picture.
Let us understand this mathematically :
Case 1: Now, taking the earth’s frame of reference, the earth seems to be stationary; hence the speed of the car is 100 km/hr.
Case 2: If the frame of reference is outside the earth’s, say, from the moon, we see the car moving at a speed of (100+1670 = 1770 km/hr); adding the car’s speed and the earth’s rotational speed.
Case 3: Now, if we take our frame of reference considering the sun, we get the car’s speed as 100+1670+108000 = 109770 km/hr; adding the speed of the car, the earth’s rotational speed, and the earth’s orbital speed around the sun.
Now, the car is moving at a considerable speed, but the car does not appear to be at high speed. It only seems at 100 km/hr because of the frame of reference. Since the observer is in the frame of reference inside the earth, the earth is stable for the observer.
Types of Frames of Reference:
- Inertial Frame of Reference.
- Non-inertial Frame of Reference.
Inertial Frame of Reference
For an inertial frame of reference, Newton’s law holds valid. This means that if no external (outer) force is acting on a body, it will remain at rest or in the same (uniform) motion. Assume an object is held on the earth’s surface; it is at rest for someone looking at it from the earth, while it is in motion for someone looking at it from the moon; what is my inertial frame in this case? The inertial frame of reference is relative because we regard a reference frame as the inertial frame of reference first. An inertial frame could be defined in a broader sense as, concerning the predicted inertial reference frame, the inertial frame is either stationary or moves at a constant velocity.
Examples:
- Our planet.
- With the earth, a space shuttle moves at a constant speed.
- With the earth, a rocket moves at a constant velocity.
Non-Inertial frame of reference
Let us now define a non-inertial frame as accelerated concerning the assumed inertial frame of reference. Newton’s law will not apply to these frames. So, in the preceding example, if I consider the earth an inertial reference frame and the moon a non-inertial reference frame, this is an accelerated motion concerning the earth. If we want to make Newton’s law, we must first establish a pseudo force.
Examples:
- The frame could travel in a straight path but increase or decrease its speed.
- The frame could be moving at a constant pace along a curved course.
- The frame could speed up or slow down as it travels along a curving path.
Conclusion:
One of the main theories of kinematics is the frame of reference. Kinematics provides information on the nature of the body’s movement in a specific situation based on a frame of reference. This frame of reference is also used to study relative motion between two bodies. Overall, the frame of reference is merely the beginning of a vast pool of intriguing topics such as mechanics.
