Slide 1 : PROF. ARDAMAN SIDHU
HKSIS
PRESENTS
LECTURES IN PHYSICS
In collaboration with
Wiziq.com
Slide 2 : TIME: 6.00 p. m.
ANGULAR DISPLACEMENT : ANGULAR DISPLACEMENT Angular displacement of the object moving around a circular path is defined as the angle traced out by the radius vector at the centre of the circular path in a given time.
ANGULAR DISPLACEMENT : ANGULAR DISPLACEMENT Angular displacement is a vector quantity provided it is small .
Its direction depends upon the sense of rotation of the object and can be given by Right Hand Rule;
The rule states that if the curvature of the fingers of right hand represents the sense of rotation of the object, then the thumb, held perpendicular to the curvature of the fingers, represents the direction of angular displacement vector.
ANGULAR VELOCITY : ANGULAR VELOCITY Angular velocity of an object in circular motion is defined as the time rate of change of its angular displacement. It is generally denoted by (O) and is measured in radians per second.
ANGULAR VELOCITY : ANGULAR VELOCITY The direction , of angular velocity ? according to Right hand rule is along the axis of circular path directed upwards.
RELATION BETWEEN LINEAR VELOCITY AND ANGULAR VELOCITY : RELATION BETWEEN LINEAR VELOCITY AND ANGULAR VELOCITY RELATION BETWEEN LINEAR VELOCITY AND
ANGULAR VELOCITY
ANGULAR ACCELERATION : ANGULAR ACCELERATION ANGULAR
ACCELERATION
RELATION BETWEEN LINEAR ACCELERATION AND ANGULAR ACCELERATION
UNIFORM CIRCULAR MOTION : UNIFORM CIRCULAR MOTION When a point object is moving on a circular path with a constant speed., then the motion of the object is said to be a uniform circular motion.
Frequency. In circular motion, the frequency is defined as the number of revolutions completed by the object on its circular path in a unit time.
Relation between angular velocity, frequency and time period.
CENTRIPETAL ACCELERATION : CENTRIPETAL ACCELERATION The uniform circular motion is an example of accelerated motion.
Acceleration acting on the object undergoing uniform circular motion is called centripetal acceleration.
Expression for centripetal acceleration
CENTRIPETAL ACCELERATION : CENTRIPETAL ACCELERATION Direction of centripetal acceleration.
The centripetal acceleration vector acts along the radius of the circular path at that point and is directed towards the centre of the circular path.
TANGENTIAL ACCELERATION AND CENTRIPETAL ACCELERATION : TANGENTIAL ACCELERATION AND CENTRIPETAL ACCELERATION A particle describing a circular path of radius r with centre at O. Let the linear speed of the particle be changing with time.
The particle has two types of accelerations.
1. Centripetal acceleration (ac)=
It acts along the radius and is directed towards the centre of the circular path.
2. Tangential acceleration (aT) = ra .
It acts along the tangent to the circular path and in the plane of the circular path.
TANGENTIAL ACCELERATION AND CENTRIPETAL ACCELERATION : TANGENTIAL ACCELERATION AND CENTRIPETAL ACCELERATION are perpendicular to each other.
CONCEPT OF CENTRIPETAL FORCE : CONCEPT OF CENTRIPETAL FORCE DYNAMICS OF UNIFORM CIRCULAR MOTION—CONCEPT OF CENTRIPETAL FORCE
Centripetal force is the force required to move a body uniformly in a circle. This force acts along the radius and towards the centre of the circle.
we have already obtained an expression for centripetal acceleration as
a = v ?
As F = m a, therefore, centripetal force = mass x centripetal acceleration
i.e.
CONCEPT OF CENTRIFUGAL FORCE : CONCEPT OF CENTRIFUGAL FORCE CENTRIFUGAL FORCE is a force that arises when a body is moving actually along a circular path, by virtue of tendency of the body to regain its natural straight line path.
Centrifugal force can be regarded as the reaction of centripetal force.
Centrifugal force acts along the radius and away from the centre of the circle.
CONCEPT OF CENTRIPETAL &CENTRIFUGAL FORCE : CONCEPT OF CENTRIPETAL &CENTRIFUGAL FORCE Note that centripetal and centrifugal forces, being the forces of action and reaction act always on different bodies.
For example, when a piece of stone tied to one end of a string is rotated in a circle, centripetal force F1 is applied on the stone by the hand.
In turn, the hand is pulled outwards by centrifugal force F2.
ROUNDING A LEVEL CURVED ROAD : ROUNDING A LEVEL CURVED ROAD The weight of the car, mg, acting vertically downwards,
Normal reaction R of the road on the car, acting vertically upwards.
Frictional force F, acts along the surface of the road, towards the centre of the turn, as explained already.
As there is no acceleration in the vertical direction,
R – mg = 0 or R = mg
ROUNDING A LEVEL CURVED ROAD : ROUNDING A LEVEL CURVED ROAD The centripetal force required for circular motion is along the surface of the road, towards the centre of the turn.
ROUNDING A LEVEL CURVED ROAD : ROUNDING A LEVEL CURVED ROAD If h is height of centre of gravity of vehicle above the road, and 2 x is the distance between the front wheels or the back wheels, the for no overturning, moments of forces about A must be equal and opposite.
for no overturning.
BANKING OF ROADS : BANKING OF ROADS This phenomenon of raising outer edge of the curved road above the inner edge is called banking roads.
BANKING OF ROADS : BANKING OF ROADS Discussion
1.Maximum possible speed of a car on a banked road is greater than that on a flat/unbanked road.
2. If , i.e., if banked road is perfectly smooth, then from equation
At this speed, frictional force is not needed to provide the necessary centripetal force. Driving at this speed on a banked road will cause almost no wear and tear of the tyres.
BENDING OF A CYCLIST : BENDING OF A CYCLIST When a cyclist takes a turn, he also requires some centripetal force. If he keeps himself vertical while turning, his weight is balanced by the normal reaction of the ground. In that event, he has to depend upon force of friction between the tyres and the road for obtaining the necessary centripetal force.
BENDING OF A CYCLIST : BENDING OF A CYCLIST To avoid dependence on force of friction for obtaining centripetal force, the cyclist has to bend a little inwards from his vertical position.
A component of normal reaction in the horizontal direction provides the necessary centripetal force.
Motion in a vertical circle : Motion in a vertical circle The motion of a small body tied to one end of a string and whirled in a vertical circle.
At any time t, let the body be at P at angular position , shown in fig.
Motion in a vertical circle : Motion in a vertical circle Tension in string at any time
At Lowest point . h= 0
At highest point h = 2r
The body will move along the vertical circle only when
TH 0.
For looping the loop
Hence for looping the vertical loop, the minimum velocity at the lowest point L is
Motion in a vertical circle : Motion in a vertical circle And minimum value of velocity at the highest point is
And
PRACTICAL APPLICATIONS OF MOTION IN A VERTICAL CIRCLE : PRACTICAL APPLICATIONS OF MOTION IN A VERTICAL CIRCLE When a bucket containing water is rotated in a vertical circle with a velocity at the lowest point,
, water shall not spill even at the highest point.
PRACTICAL APPLICATIONS OF MOTION IN A VERTICAL CIRCLE : PRACTICAL APPLICATIONS OF MOTION IN A VERTICAL CIRCLE A pilot of an aircraft can successfully loop a vertical loop without falling at the top of the loop when its velocity at the bottom of the loop is
NUMERICALS : NUMERICALS A stone tied to the end of a string 60 cm long is whirled in horizontal circle with a constant speed. If the stone makes 12 revolutions in 25s, what is magnitude and direction of acceleration of stone ?
[Ans= 5.47 m/sec2]
NUMERICALS : NUMERICALS A cyclist is riding with a speed of 36 km/hr As he approaches a circular turn on the road of radius 50m, he applies brakes and reduces his speed at constant rate of 0.5 m/s2. What is the magnitude and direction of net acceleration of cyclist on circular road ?
Ans: and is given
= 2.06 m/s2
Slide 31 : For all your Physics Problems
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