Explain translatory motion and give examples of various types of translatory motion.

Difficulty: Medium

Translatory motion:

In translation motion, a body moves along a line without any rotation. The line may be straight or curved.

Examples:

Riders moving on the Ferris wheel are also in translational motion. Their motion is in a circle without rotation.

Types of Translatory motion:

Translatory motion can be divided into linear motion, circular motion, and random motion.

1. Linear motion:

The straight-line motion of a body is called linear motion.

Examples:

The motion of objects such as a car moving on a straight and level road is linear motion.

Airplanes flying straight in the air and objects falling vertically down are also examples of linear motion.

2. Circular motion:

The motion of an object in a circular path is called circular motion.

Examples:

A stone tied at the end of a string can be made to whirl. The stone moves in a circle and thus has a circular motion.

Toy train moving on a circular track. A bicycle or a car moving along a circular track possess circular motion.

The motion of the earth around the sun and the motion of the moon around the earth are also examples of circular motion.

3. Random Motion:

The disordered or irregular motion of an object is called random motion.

Examples:

The motion of insects and birds is irregular. Thus, the motion of insects and birds is random

The motion of dust or smoke particles in the air is also random.

The Brownian motion of a gas or liquid molecules along a zigzag path as shown in the figure is also an example of random motion.

Differentiate between the following:

(i)   Rest and motion

(ii)  Circular motion and rotatory motion

(iii) Distance and displacement

(iv) Speed and velocity

(v) Linear and random motion

(vi) Scalers and Vectors

Difficulty: Hard

1. Difference between Rest and motion:

Rest:

A body is said to be at rest if it does not change its position concerning its surroundings.

Motion:

A body is said to be at rest if it changes its position concerning its surroundings.

The state of rest or motion of a body is relative. For example, a passenger sitting in a moving bus is at rest because he/she is not changing his/her position concerning the other passengers or objects in the bus but to an observer outside the bus the passengers and the objects inside the bus are in motion

2. Difference between Circular and rotatory motion:

Circular motion:

Any turning as if on-axis is rotatory motion. Any rotatory motion where the radius of gyration, length, and axis of rotation is fixed is circular motion. And that is the difference. Circular motion is just a special case of rotatory motion. That is, there is no fixed axis and radius restriction for rotatory motion. But there is circular motion.

For example, all planets have rotatory motion around their suns but most of the orbits are elliptical. Therefore, the rotation axis and radius of gyration vary as they trek around. So, most, if not all, planets do not have circular motion.

Note: Gyration length:

A length that represents the distance in a rotating system between the point about which it is rotating and the point to and from which the transfer of energy has the maximum effect.

3. Difference between distance and displacement:

 Distance Displacement Length of the path between two points is called the distance between those points. Displacement is the shortest distance between two points which has magnitude and direction distance distance Distance is a scalar quantified displacement Displacementquantity distancentity Distance is denoted by “S”.             S=vt Its unit is metered (m). Displacement is denoted by “d”. d=vt Its SI unit is meter (m). Distance(S) dotted lines, Displacement(d) dark lines from point A to B.

4. Differentiate between speed and velocity

 Speed Velocity The distance covered by an object in a unit of time is called speed.    Distance=speed x time  Or  S=vt The rate of displacement of a body is called velocity.   V=d/t or d=vt Speed is a scalar quantity. Velocity is a vector quantity. SI unit ispeed is SI unit of velocity is the same as the speed

5. Difference between linear and random motion

Linear motion:

The straight-line motion of a body is called linear motion.

Examples:

The motion of objects such as a car moving on a straight and level road is linear motion.

Airplanes flying straight in the air and objects falling vertically down are also examples of linear motion.

Random Motion:

The disordered or irregular motion of an object is called random motion.

Examples:

The motion of insects and birds is irregular. Thus, the motion of insects and birds is random.

The motion of dust or smoke particles in the air is also random.

The Brownian motion of a gas or liquid molecules along a zigzag path as shown in the figure is also an example of random motion.

6. Difference between scalers and vectors:

 Scalers Vectors A scalar quantity is described completely by its magnitude only. A vector quantity is described by its magnitude and direction. Examples Examples of scalers are mass, length, time, speed, volume, work, energy, density, power, charge, pressure, area, and temperature. Examples Examples of the vector are velocity, displacement, force, momentum, torque, weight, electrical potential, etc.

Define the terms speed, velocity and acceleration

Difficulty: Easy

Speed:

The distance covered by an object in unit time is called speed.

$Speed = \frac{Distance \: covered}{Time \: taken}$

$v = \frac{S}{t}$

Velocity:

The rate of displacement of a body is called velocity.

$Velocity=\frac{Displacement}{Time \: taken}$

$v = \frac{D}{t}$

Acceleration:

Acceleration is defined as the rate of change of velocity of a body

$acceleration = \frac{Change \: of \: velocity}{Time \: taken}$

$acceleration = \frac{final \: velocity \: - \: initial \: velocity}{Time \: taken}$

$a=\frac{vf \: - \: vi}{t}$

Unit of acceleration:

SI unit of acceleration is a meter per second square.

Can a body moving at a constant speed have acceleration?

Difficulty: Easy

Yes, when a body is moving with constant speed, the body can have acceleration if its direction changes. For example, if the body is moving along a circle at a constant speed, it will have acceleration due to the change of direction at every instant.

How do riders in a Ferris wheel possess Translatory motion but not circular motion?

Difficulty: Easy

Riders in a Ferris wheel possess Translatory motion because their motion is in a circle without rotation.

Sketch a distance-time graph from the body starting from rest. How will you determine the speed of the body from this graph?

Difficulty: Medium

Distance-time graph for a body starting at rest:

When a body starts from rest, the distance-time graph is a straight line. Its slope gives the speed of the object.

Speed of a body from the graph:

Consider two points A and B on the graph

Speed of the object=slope of line AB

= Distance EF/Time CD=2

= $\frac{Distance \: EF}{Time \: CD}$

= $\frac{20m}{10s}$

= $\frac{2m}{s}$

The speed found in the graph is 2m/s

What would be the shape of a speed-time graph of a body moving with variable speed?

Difficulty: Easy

An object moving with variable speed:

When an object does not cover equal distances in equal intervals of time then its speed is not constant. In this case, the distance-time graph is not a straight line.

The slope of the curve at any point can be found from the slope of the tangent at that point. For example,

the slope of the tangent at $P=\frac{RS}{QS}$

$=\frac{30m}{10s}$

$=\frac{3m}{s}$

Thus, the speed of the object at P is $\frac{3m}{s}$

The speed is higher at instants when the slope is greater, speed is zero at instants when the slope is horizontal.

Which of the following can be obtained from the speed-time graph of a body?

(i) Initial speed

(ii)  Final speed

(iii) Distance covered in time t

(iv) Acceleration of motion

Difficulty: Easy

All the above factors can be obtained from a speed-time graph.

How can vectors quantities can be represented graphically?

Difficulty: Medium

Symbolic Representation of a vector:

To differentiate a vector from a scalar quantity, we generally use bold letters to represents vectors quantities such as F, a, d or a bar or an arrow over the symbols such as $\bar{F},\bar{a},\bar{d} \: or \: \overrightarrow{F},\overrightarrow{a} ,\overrightarrow{d}$

Graphical Representation of a vector:

A straight line is drawn with an arrowhead at one end. According to some suitable scale, the length of a line represents the magnitude and the arrowhead gives the direction of the vector.

Why vector quantities cannot be added or subtracted like scaler quantities?

Difficulty: Easy

The scaler quantities obey the rules of arithmetic and ordinary algebra because scaler quantities have no directions, so vectors obey special rules of vector algebra, therefore, vectors are added by head to tail rule (vector algebra).

How are vector quantities important to us in our daily life?

Difficulty: Medium

We use vectors in almost every activity of life. A vector is a quantity that has both direction and magnitude.

Examples of everyday activities that involve vectors include:

• Breathing (your diaphragm muscles exert a force that has magnitude and direction)
• Walking (you walk at a velocity of around 7 km/h in the direction of the bathroom)
• Going to school (the bus has a length of about 300m and is headed towards your school)
• Lunch (the displacement from your classroom to the canteen is about 50m in the north direction.
• To describe a car’s velocity, you would have to state it as 80km/h south.

Vectors are important as they describe physical processes in the real world, and without understanding them, we cannot understand how the real world works. Imagine how difficult it would be for an air traffic controller if he did not understand vectors when directing a plane's speeds and direction.

Sketch a velocity-time graph for the motion of the body. From the graph explaining each step, calculate the total distance covered by the body.

Difficulty: Medium

Velocity time graph:

Calculation of distance moved by an object from a velocity-time graph:

The distance moved by an object can also be determined by using its velocity-time graph.

1. If an object moves at constant velocity v for time t. The distance covered by the object is v x t. the distance can also be found by calculating the area under the velocity-time graph. This area is shaded and is equal to v x t.

2. If the velocity of the object increases uniformly from 0 to v in time t. the magnitude of its average.

avg. velocity = $\frac{0 \: + v}{2}$

=$\frac{v}{2}$

$Distance \: covered = average \: velocity\times \: time =\frac{1}{2v}\times \:t$

Now we calculate the area under the velocity-time graph, which is equal to the area of the triangle shaded in the figure.

Its \: value \: is \: equal \: to \: $\frac{1}{2} \: base\times \: height =\frac{1}{2} \: v\times t$

Note:

The area between the velocity-time graph and the time axis is numerically equal to the distance covered by the object.