Contents
The study of Physics Topics can help us understand and solve real-world problems, from climate change to medical imaging technology.
What is the Difference Between Translational and Rotational Forces?
In practical cases, when a body is in motion it can rotate too. When a wheel is pushed, it moves forward. At the same time it also rotates about an axis through its centre. A rain drop can vibrate while it falls. Representation of such motions are usually very complex.
To avoid this complexity, an object is often taken as a geometrical point, ignoring its shape or size. This geometrical point is called a particle. In case of linear motion, the properties of the particle and of the object are identical and so discussion about the motion of the particle is sufficient to describe the motion of the object.
To describe the motion of objects, sometimes we consider a body to be composed of many particles. In such cases, we do not consider a geometrical point but the aggregation of many particles.
Translation: If a body moves along a straight line, its motion is called translation. Motion of a freely falling body or the motion of a car along a straight road, are examples of translational motion.
Characteristics of translation:
i) The direction of motion remains the same.
ii) The particles of an object under translatory motion traverse equal lengths in equal intervals of time and they also move parallel to one another. As in Fig., AA‘A” BB’B” and CC’C” lines are parallel and equal.
iii) Lines joining any two particles of the body in translation remain parallel to one another for any position of the object. Observe, the lines AB, A’B’ and A”B” are parallel to one another.
The motion of any particle along a curved line can be con-sidered as the aggregate of number of infinitesimally small translatory motions.
Rotation: When an object moves in a circular path about a fixed point or an axis, the motion is called rotation. The axis is called the axis of rotation. Fig. shows some examples of rotation. However, the axis may be located outside the object [Fig.(a)].
Characteristics of rotation:
- Each constituent particle of a rotating body rotates by an equal angle in a fixed interval of time.
- Axis of rotation always remains stationary.
Complex motion: If a body exhibits translational as well as a rotational motion simultaneously, then it is said to be in a state of complex motion.
Example:
i) The wheel of a running car executes a complex motion. The wheel rotates around the axis through its centre (rotation) and moves forward along the road (transla-tion).
ii) The earth rotates around its own axis and at the same time it revolves around the sun following an elliptical path. As the orbit is elliptical the earth sometimes comes close to the sun and sometimes moves away from it. So, the earth also exihibits a complex motion.
Comparison between translation and rotation:
- Translation is motion in a straight line, whereas rotation is a circular motion in a plane.
- In translation, the direction of motion is fixed. In rotation, the axis of rotation is fixed.
- Translation of each constituent particle of the body is the same during the movement of the body. In rotation, constituent particles of the body at larger distances from the axis of rotation describe larger distances.
Some Physical Quantities Related to Motion
Relative to a definite frame of reference, a body may be at rest, or in any form of motion like translation, rotation, vibration etc. For the convenience of kinematical study of rest and motion of a body, a few important physical quantities are defined. These are the essential properties that represent the states of rest and motion of a body, and their measured values furnish the exact physical state.
Position
Let an object be located at the point A [Fig.]. To measure the position of the object, and to express it in a well-defined manner, we have to
- choose a reference point, i.e., an origin—the point O is this origin in Fig.;
- measure the linear distance OA; and
- specify the direction of A relative to the origin O.
This would always lead to statements like : ‘the object A is situated 5 m east of the origin O’, or ‘the object B is 2 m north-east of O’. In short, we may write \(\overrightarrow{O A}\) = 5 m towards east; \(\overrightarrow{O B}\) = 2 m to the north-east.
These statements define the positions of the objects at A and at B. It is important to note that, each statement includes the magnitude of the linear distance, as well as the
direction, relative to the origin.
Definition: The position of an object is defined as linear distance as well as its direction with respect to a pre-assigned reference point.
Position is a vector quantity: As per the definition, position is a physical quantity having both magnitude and direction. So it is a vector quantity (discussed in detail in the chapter Vector). It is often called the position vector, and denoted by the symbol \(\vec{r}\).
In the above examples, position of A: \(\overrightarrow{r_1}\) = 5 m east; position of B: \(\overrightarrow{r_2}\) = 2 m north-east.
Another interesting point is that, to find the position of B relative to A (\(\overrightarrow{A B}\) in Fig.), a simple numerical calculation, using the values 5 m and 2 in, is not sufficient.
The directions are to be considered as well. This technique leads to a new branch in mathematics, known as vector algebra (see the chapter Vector).
Units and dimension: The magnitude of the position vector is actually a distance. It has the units of length.
Similarly, the dimension of the position vector is that of length, i.e., its dimension = L.