**FUNDAMENTALS OF MOTION**

Many scientists have studied motion and its properties because of its importance to life. The Italian, Galileo Galilei, who lived from 1564 to 1642, did the first systematic study of motion. The science of the study of motion done by Galileo is known as kinematics. Isaac Newton was another scientist who did detailed work on the study of motion.

Table of Contents

Motion involves a change of position of a body with time. It also involves how things move and what makes them to move. Kinematics is the description of how objects move without regard to forces causing their motion, and dynamics deals with why objects move as they do.

__ __

**TYPES OF MOTION**

There are four basic – types of motion. There are as follows.

- TRANSLATIONAL MOTION:- When a body moves from a point A, along the line AB to another point B (see Fig. 4.1), we say that the body is translated from A to B, and the motion performed is known as translational motion. For example when an aeroplane flies from Abuja to Lagos or a car travels from Lagos to Enugu

- OSCILLATORY MOTION: In this type of motion, a body moves to and fro, about a fixed point. Examples are the vibration of a plucked guitar string, the motion of a pendulum as it swings back and forth, the vibration of the molecules of a solid.

__ __

- RANDOM MOTION: In this type of motion, the body moves in zigzag direction continuously so that they do not trace definite path. This type of motion is exhibited by molecules in gases. Other examples of random motion is the Brownian motion – an irregular motion of particles of various kinds suspended in water or smoke particles suspended in air t.c
- ROTATIONAL MOTION: This is the motion of a body which travels in a circle or ellipse and rotates about an axis. Examples are (i) the rotation of the earth about its axis (ii) the rotation of blades of an electric fan about its axis (iii) the rotation of a tap about a central axis.

RELATIVE MOTION

If two bodies, A and B are moving on a straight line, the velocity of A relative to B is found by adding the Velocity of B revered to the velocity of A. For instance, if a car traveling on a straight road at 100km/hr passes a bus going in the same direction at 60km/hr, the velocity of the car relative to the bus is (-60+100) = 40km/hr. If the car and the bus are traveling in opposite direction with the same velocities of 100km/r and 60km/hr respectively, the velocity of the car relative to the bus is ( -(-60) + 100) = (60 +100) = 160 km/hr.

NB: When the velocities are not in the same straight line, the parallelograms law should be used to add this since velocities are vectors, and their magnitudes and direction must be taken into consideration.

** **

## CAUSES OF MOTION

We have been describing the motion of a body without regard to what causes the motion. A block of wood resting on a table will remain at rest until it is pushed or pulled by an agent. Such an agent that change or tends to change the state of rest or uniform motion in a straight line of a body is called **force**.

__ __

## TYPES OF FORCE

There are two main types of forces, contact force and force field.

- CONTACT FORCE: This may be regarded as a force which exists between surfaces in contact. It includes pushing and pulling forces, frictional forces, reaction and tension forces in strings and wires.
- FORCE FIELDS: These are forces whose sources do not require contact with the body to which they are applied. Examples are gravitational force, electrostatic and magnetic forces

__ __

**EVALUATION**

- Explain the types of motion.
- Differentiate between contact & field force.

__ __

## SIMPLE IDEA OF CIRCULAR MOTION

An object moving with a constant speed along a circular path is said to have a uniform circular motion. Examples are the moon circling the earth, the planets moving round the sun, earth moving round the sun, stone tied to a string which is whirled in a horizontal vertical circle.

Circular motion has three characteristics:

- constant speed (2) changing or variable velocity (3) centripetal acceleration.

The acceleration that is directed towards the centre of the circular path is known as centripetal acceleration. Its magnitude a is given by

Where V is the uniform speed and r is the radius of the circular path.

Centripetal force F_{T} is defined as that inward force required to keep an object moving with a constant speed in a circular path

The centripetal force is given by where m is the mass of the object moving with a uniform velocity v in a circular path or radius r.

__ __

* Centrifugal force:* The centrifugal force is the reaction force that tends to move a body away from the centre. In other words, it acts in opposite direction to the centripetal force

__ __

* Centrifuge:* A centrifuge is a device used to separate particles in suspension from the liquid in which they are contained.

**EVALUATION **

- Differentiate between centripetal & centrifugal force.
- A stone tied to a string is made to revolve in a horizontal circle of radius 4m with an angular speed of 2 rad/s. With what is tangential velocity will the stone move off the circle if the string cuts?

** **

**READING ASSIGNMENT**

www.google.com(click on google search, type “circular motion”,click on search) & – New school physics by M.W.Anyakoha,Phd. Pg 12-27

**WEEKEND ASSIGNMENT**

- Which of the following types of motion does a body undergo when moving in a haphazard manner? (a) Random motion (b) Translatory motion (c) Rotational motion (d) Vibratory motion
- What type of motion does the skin of a talking drum perform when it is struck with a drum stick? (a) Rotational (b) Translational (c) Random (d) Vibratory
- The motion of the prongs of sounding turning fork is

(a) rotational (b) vibratory (c) vibratory and rotational (d) random

- A body moves with a constant speed but has an acceleration. This is possible if it

(a) moves in a straight line (b) moves in a circle (c) is oscillating

(d) is in equilibrium (e) has a varying

- A body moves along a circular path with uniform angular speed of 0.6rads
^{−1}and at a constant speed of 3.0ms^{−1}. Calculate the acceleration of the body towards the centre of the circle.

(a) 25.0ms^{−2} (b) 5.4ms^{−2} (c) 5.0ms^{−2} (d) 1.8ms^{−2}

- The angular speed of an object describing a circle of radius 4m with a linear constant speed of 10ms
^{−1}is (a) 40rads^{−1}(b) 14rads^{−1}(c) 2.5rads^{−1}(d) 0.40rad^{−1} - A body moving at a constant speed accelerates when it is in (a) rectilinear motion

(b) translational motion (c) circular motion (d) vibrational motion

- The study of motion without involving the force which causes the motion is called

(a) kinematics (b) inertia (c) electromagnetic (d) dynamics

- The magnitude of the force required to make an object of mass M move with speed V in a circular path of radius R is given by the expression

(a) (b) (c) (d)

- 10
**.**The following are types of motion except (A) random motion (b) rotational motion (c) nuclear motion (d) oscillatory motion. - 11
**.**The motion of the prongs of a sounding turning fork is (a) random (b) translational (c) rotational (d) vibratory - 12
**.**A body moving in a circle at constant speed has - a velocity tangential to the circle
- a constant kinetic energy

- an acceleration directed towards the circumference of the circle. Which of the statement above are correct

(a) i & ii only (b) ii & iii only (c) I & iii only (d) i, ii & iii

- 13
**.**A loaded test – tube which floats upright in water is carefully and slightly depressed and then which of the following best describes the subsequent motion of the test tube (a) circular (b) rotational (c) random (d) oscillatory. - 14
**.**Which of the following correctly gives the relationship between linear speed v & angular velocity w of a body moving uniformly (a) v=w r (b) v=w^{2}r (c) v=wr^{2 }(d) v=w/r

__ __

**THEORY**

- Mention and describe two practical situations where centripetal force must be taken into account.
- A body weighing 100N with a speed of 5ms
^{-1}in a horizontal circular path of radius 5m. Calculate the magnitude of the centripetal force acting on the body (g= 10ms^{-2}). (WAEC, 1999) - A piece of stone attached to one end of spring is whirled round in a horizontal circle of radius 7m. When the constant speed of the stone is 40ms
^{-1}, calculate the centripetal acceleration. - A keke (tricycle) moves around Mary Slessor roundabout of radius 50m, at a constant speed of 20ms
^{-1}, find (a) Centripetal acceleration (b) Centripetal force - A particle of mass 100kg is fixed to the tip of a fan blade which rotates with angular velocity of 100rads
^{-1}. If the radius of the blade is 0.2m, find the centripetal force. - 6. A body of mass 5kg moving in a circular path with a velocity of 5m/s for 10 complete revolution within 4s. If the radius of the circular path is 30m. Find (a) the centripetal force (b) the centripetal acceleration (c) angle subtended in radian (d) angular velocity

See also