- A person on the ground sees the ball move in a circle due to centripetal force (tension in the string).
- A person on the rotating platform sees the ball as stationary only if they assume an opposite force to balance the tension.
- When the string breaks, the ground observer sees the ball go straight, while the rotating observer sees it move outward, due to the assumed centrifugal force.
Definitions [22]
Definition: Non-Linear Motion
"The motion of an object that does not move in a straight line is called ‘non-linear motion’."
Definition: Linear motion
A train or a moving vehicle on a road may travel in a straight line or in the same direction. This motion of an object is called linear motion. An object in linear motion shows displacement along a straight line."
Define Displacement.
Displacement of an object between two points is the shortest distance between these two points.
“It is the unique path that can take the body from its initial to the final position.”
The displacement of a moving body is defined as the change in its position along a particular direction
Displacement
- Displacement is the shortest distance in a straight line between the starting point and the final point, along with a direction. It is a vector quantity, meaning it includes both magnitude (distance) and direction.
- Example: In Ranjit’s case, the displacement is the straight line AD from his house to the school.
Distance
- Distance is the total length of the path travelled by a moving object, regardless of the direction. It is a scalar quantity, which means it only has magnitude (size), not direction.
- Example: If Ranjit walks from point A to B to C to D, the distance is the total of AB + BC + CD.
Define Distance.
The length of path travelled by a body in certain interval of time is called distance.
Define speed Mention its formula and unit.
Speed is the rate of change of distance.
Formula: Speed = distance /time
Unit is meter/second (m/s)
Define Speed.
The distance covered by a body in a unit time is called its speed. It is also defined as the rate of change position of a body in any direction.
Speed = distance/time
Define Velocity.
“Rate of change of displacement with time is called velocity.”
OR
“The time rate of change of displacement of an object is called the velocity.”
V = distance/time
Define velocity.
Velocity is the rate of change of displacement. It is the displacement in unit time.
Define velocity Mention its formula and unit.
Velocity is the rate of change in displacement.
Formula: Velocity (v) = displacement / time
SI unit of velocity is meter / second (m/s).
Define Uniform circular motion.
When a particle moves with a constant speed in a circular path, its motion is said to be the uniform circular motion.
Define angular velocity.
Angular velocity of a particle is the rate of change of angular displacement.
Definition: Angular Displacement
The angle traced out by the radius vector at the centre of the circular path in a given time, expressed as Δθ = θ2 − θ1, is called angular displacement.
Definition: Angular Velocity (ω)
The rate of change of angular displacement of a body undergoing circular motion is called angular velocity.
Definition: Angular Acceleration (α)
The rate of change of angular velocity of a body is called angular acceleration.
Definition: Radial (Centripetal) Acceleration
The component of acceleration directed towards the centre of the circular path is called centripetal acceleration (or radial acceleration).
Definition: Centripetal Force
The force directed towards the centre along the radius, required to keep a body moving along a circular path at constant speed, is called centripetal force.
Definition: Uniform Circular Motion
When a particle moves with a constant speed in a circular path, its motion is said to be uniform circular motion.
OR
The motion of a body moving with constant speed along a circular path is called uniform circular motion.
OR
The motion of a body moving with constant speed along a circular path, where the velocity is always tangential to the circular path and remains constant in magnitude, is called uniform circular motion.
Definition: Centripetal Force
A force that acts on any object moving along a circle and is directed towards the centre of the circle. When this force stops acting, the object flies off along a straight line (tangent to the circle) in the direction of its velocity at that instant.
Definition: Fictitious Force
A force which really does not exist, but is considered to describe (or understand) a certain motion, is called a fictitious force (or virtual force).
Definition: Centrifugal Force
A force assumed (by an observer moving with the body) to be acting on the body in a direction away from the centre of a circular path is called centrifugal force.
Formulae [2]
Formula: Centripetal Force
F = \[m\omega^{2}r=\frac{mv^{2}}{r}\] = mωv
where:
- F = Centripetal force (in Newtons)
- m = Mass of the object (in kg)
- ω = Angular speed (in rad/s)
- r = Radius of the circular path (in m)
- v = Linear speed or tangential velocity (in m/s)
Formula: Centripetal Acceleration
a = ω2r = \[\frac {v^2}{r}\] = ωv
where:
-
a = Centripetal acceleration (in m/s²)
Key Points
Key Points: Uniform Circular Motion
- In UCM, speed is constant, but velocity continuously changes direction, always remaining tangential to the path.
- Angular displacement is the angle swept by the radius vector; angular velocity is its rate of change.
- Even at constant speed, centripetal acceleration is never zero — it always acts towards the centre of the circular path.
- Centripetal force is always directed towards the centre and is essential to maintain circular motion — it does no work on the body.
- If speed is constant in circular motion, tangential acceleration = 0, but radial acceleration ≠ 0.
Key Points: Centrifugal Force
Concepts [14]
- Force and Motion
- Types of Motion
- Multiple Motion
- Distance and Displacement
- Speed
- Velocity
- Acceleration and Retardation
- Displacement - Time Graph Or Distance - Time Graph
- Velocity - Time Graphs
- Equations of Motion by Graphical Method
- Motion of Freely Falling Body
- Uniform Circular Motion (UCM)
- Centripetal Acceleration
- Centrifugal Forces
