INTRODUCTION
CIRCULAR
Physics deals with various types of motions In daily life we come across various practical situations involving motion Cyclist travelling tight road perform rectilinear (linear motion A cyclist taking turn along a curved road perform a curvilinear motion. A cyclist moving along a circular race course track perform a circular motion.
desc cent
The circular motion is a special case of linear or translatory motion, in which particle revolves along circumference of a circle
Following are some examples of a circular
motion.
Motion of earth and other planets around the Motion of roller coaster looping the loop
sun Motion of an object tied at the end of a string and whirled in a circle
Motion of up of minute hand hour hand and second hand of a clock
ANGULAR DISPLACEMENT:
Consider a particle revolving along the circumference of a circle of radius in anticlockwise sense A vector drawn from the center of circle to the position of particle on circumference of circle is called as 'radius vector It is also called as position vector only if one chooses origin at center The direction of radius vector changes as position of particle changes. When particle performing circular motion is at A. the radius vector is Consider a particle performing circular motion.
ACCELERATION IN UNIFORM CIRCULAR MOTION RADIAL ACCELERATION TION
of .
Acceleration is the time rate of change of velocity Velocity is a vector quantity, which requires both magnitude and direction for its complete description. The velocity of moving particle changes. if there is either change in magnitude of velocity or change in direction of velocity or change in both the magnitude and direction of velocity. In UCM, the magnitude of velocity is constant, however the direction of velocity goes on changing continuously Hence U.C.M. is an accelerated motion. The acceleration of a particle performing U.C.M can be obtained by geometrical method and calculus method.
1.6 CENTRIPETAL FORCES
AND
CENTRIFUGAL
In uniform circular motion there is no change in magnitude of velocity, but there is only change in direction of velocity
Hence uniform circular motion is an accelerated motion According to Newton's second law of motion, there must be a force acting on body to produce an acceleration. This force must act within the direction of acceleration, i.e. along radius and directed towards the centre of circle. Such a force acting on particle performing circular motion is called as centripetal force. Centripetal force is necessary for particle to perform circular motion.
Centripetal force is force acting on particle performing circular motion., which is along radius of circle and directed towards the centre of circle. Since centripetal force acts at right angles to the tangential velocity of particle, there is no displacement in the direction of force, hence no work
is done by centripetal force.
As per Newton's second law of motion. Force = mass x acceleration
Here, Fcp = ma
a = vto =
Fcp = me = " =mru? (1.40)
In vector notation,
Fer FCP = = -ma .(1.41)
where m-mass of particle performing U.C.M.
linear speed of particle performing U.C.M.
U CIU Since centripetal force acts at right angles to the tangential velocity of particle, there is no
displacement in the direction of force, hence no work is done by centripetal force.
As per Newton's second law of motion. Force = mass x acceleration
Here, FCP = ma
a = vo = = ro
FCP = mvw = = = = mro .(1.40)
In vector notation,
Fer FCP
-mv
7 =-mo7.(1.41)
where m-mass of particle performing U.C.M. v - linear speed of particle performing U.C.M.
radius of circle,
radius vector
angular speed of particle performing circular motion
unit vector in the direction of 7 The SI unit of centripetal force is newton (N).
In nutshell, the centripetal force is a real force acting on particle performing
circular motion
is a necessary force for maintaining circular motion.
its direction is different at different points. acts along the radius of circle and directed towards the centre of circle.
INTRODUCTION
CIRCULAR
Physics deals with various types of motions In daily life we come across various practical situations involving motion Cyclist travelling tight road perform rectilinear (linear motion A cyclist taking turn along a curved road perform a curvilinear motion. A cyclist moving along a circular race course track perform a circular motion.
desc cent
The circular motion is a special case of linear or translatory motion, in which particle revolves along circumference of a circle
Following are some examples of a circular
motion.
Motion of earth and other planets around the Motion of roller coaster looping the loop
sun Motion of an object tied at the end of a string and whirled in a circle
Motion of up of minute hand hour hand and second hand of a clock
ANGULAR DISPLACEMENT:
Consider a particle revolving along the circumference of a circle of radius in anticlockwise sense A vector drawn from the center of circle to the position of particle on circumference of circle is called as 'radius vector It is also called as position vector only if one chooses origin at center The direction of radius vector changes as position of particle changes. When particle performing circular motion is at A. the radius vector is Consider a particle performing circular motion.
ACCELERATION IN UNIFORM CIRCULAR MOTION RADIAL ACCELERATION TION
of .
Acceleration is the time rate of change of velocity Velocity is a vector quantity, which requires both magnitude and direction for its complete description. The velocity of moving particle changes. if there is either change in magnitude of velocity or change in direction of velocity or change in both the magnitude and direction of velocity. In UCM, the magnitude of velocity is constant, however the direction of velocity goes on changing continuously Hence U.C.M. is an accelerated motion. The acceleration of a particle performing U.C.M can be obtained by geometrical method and calculus method.
1.6 CENTRIPETAL FORCES
AND
CENTRIFUGAL
In uniform circular motion there is no change in magnitude of velocity, but there is only change in direction of velocity
Hence uniform circular motion is an accelerated motion According to Newton's second law of motion, there must be a force acting on body to produce an acceleration. This force must act within the direction of acceleration, i.e. along radius and directed towards the centre of circle. Such a force acting on particle performing circular motion is called as centripetal force. Centripetal force is necessary for particle to perform circular motion.
Centripetal force is force acting on particle performing circular motion., which is along radius of circle and directed towards the centre of circle. Since centripetal force acts at right angles to the tangential velocity of particle, there is no displacement in the direction of force, hence no work
is done by centripetal force.
As per Newton's second law of motion. Force = mass x acceleration
Here, Fcp = ma
a = vto =
Fcp = me = " =mru? (1.40)
In vector notation,
Fer FCP = = -ma .(1.41)
where m-mass of particle performing U.C.M.
linear speed of particle performing U.C.M.
U CIU Since centripetal force acts at right angles to the tangential velocity of particle, there is no
displacement in the direction of force, hence no work is done by centripetal force.
As per Newton's second law of motion. Force = mass x acceleration
Here, FCP = ma
a = vo = = ro
FCP = mvw = = = = mro .(1.40)
In vector notation,
Fer FCP
-mv
7 =-mo7.(1.41)
where m-mass of particle performing U.C.M. v - linear speed of particle performing U.C.M.
radius of circle,
radius vector
angular speed of particle performing circular motion
unit vector in the direction of 7 The SI unit of centripetal force is newton (N).
In nutshell, the centripetal force is a real force acting on particle performing
circular motion
is a necessary force for maintaining circular motion.
its direction is different at different points. acts along the radius of circle and directed towards the centre of circle.
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