- 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 [10]
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.
Define angular velocity.
Angular velocity of a particle is the rate of change of angular displacement.
Definition: Radial (Centripetal) Acceleration
The component of acceleration directed towards the centre of the circular path is called centripetal acceleration (or radial acceleration).
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.
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: 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: 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.
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).
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
Important Questions [32]
- If the Angular Speed of the Earth is 7.26 x 10^–5 Rad/S and Radius of the Earth is 6,400 Km, Calculate the Change in Weight of 1 Kg of Mass Taken from Equator to Pole.
- Calculate the Weight of a Body Of Mass 100 Gram at Attitude 25°.
- What is the value of tangential acceleration in U.C.M.?
- Two parallel plates separated by distance d are kept at potential difference V volt. A charge q of mass m enters in parallel plates with some velocity. The acceleration of the charged particle will be
- The Spin Dryer of a Washing Machine Rotating at 15 R.P.S. Slows Down to 5 R.P.S. After Making 50 Revolutions. Find Its Angular Acceleration
- When the Angular Acceleration of a Rotating Body is Zero, Which Physical Quantity Will Be Equal to Zero?
- A particle rotates in U.C.M. with tangential velocity V along a horizontal circle of diameter ‘D' . Total angular displacement of the particle in time 't' is
- Draw a Neat Labelled Diagram of Conical Pendulum. State the Expression for Its Periodic Time in Terms of Length.
- In U. C. M (Uniform Circular Motion), Prove the Relation V = W x R, Where Symbols Have Their Usual Meanings.
- Obtain an Expression for Linear Acceleration of the Particle Performing Non-uniform Circular Motion.
- A Vehicle is Moving on a Circular Track Whose Surface is Inclined Towards the Horizon at An Angle of 10°. the Maximum Velocity with Which It Can Move Safely is 36 Km / Hr. Calculate The Length
- In Circular Motion, Assuming V = W * R , Obtain an Expression for the Resultant Acceleration of a Particle in Terms of Tangential and Radial Component.
- A Particle of Mass M, Just Completes the Vertical Circular Motion. Derive The Expression for the Difference In Tensions at the Highest and the Lowest Points.
- Explain the Concept of Centripetal Force.
- A Racing Car Completes 5 Rounds of a Circular Track in 2 Minutes. Find the Radius of the Track If the Car Has Uniform Centripetal Acceleration of π2 M/S2.
- Calculate the Centripetal Force ?
- Distinguish Between Centripetal and Centrifugal Force
- A Stone of Mass 1 kg is Whirled in Horizontal Circle Attached at the End of a 1 m Long String. If the String Makes an Angle of 30º with Vertical, Calculate the Centripetal Force Acting on the Stone.
- The Bulging of Earth at the Equator and Flattening at the Poles is Due to
- A Body of Mass ‘M’ Performs Uniform Circular Motion Along a Circular Path of Radius ‘R’ With Velocity ‘V’. If Its Angular Momentum is L, Then the Centripetal Force Acting on It is
- A Coin Kept at a Distance of 5cm from the Centre of a Turntable of Radius 1.5m Just Begins to Slip When the Turntable Rotates at a Speed of 90 R.P.M.
- Write the Necessary Equation for Maximum Safety, Speed and State the Significance of Each Term Involved in It.
- A falt curve on a highways has a radius of curvature 400 m. A car goes around a curve at a speed of 32 m/s.
- Draw a Diagram Showing All Components of Forces Acting on a Vehicle Moving on a Curved Banked Road.
- Obtain Expressions of Energy of a Particle at Different Positions in the Vertical Circular Motion.
- The Difference in Tensions in the String at Lowest and Highest Points in the Path of the Particle of Mass 'M' Performing Vertical Circular Motion is
- A Planet is Revolving Around a Star in a Circular Orbit of Radius R with a Period T. If the Gravitational Force Between the Planet and the Star is Proportional to
- A Particle of Mass M Performs the Vertical Motion in a Circle of Radius R. Its Projectile Energy at the Highest Point is _______
- The Speed Limit for a Vehicle on Road is 120 Km/ Hr. a Policeman Detects a Drop of 10% in the Pitch of Horn of a Car as It Passes Him. is the Policeman Justified in Punishing the Car Driver for Crossing the Speed Limit
- If the Difference in Velocities of Light in Glass and Water is 2.7 X 10 ^7 M/S, Find the Velocity of Light in Air.
- Let Velocity of a Sound Wave Be 'V' and 'ω' Be Angular Velocity. the Propagation Constant of the Wave is
- A Stone of Mass 5 kg. Tied to One End of a Rope of Length 0.8m, is Whirled in a Vertical Circle. Find the Minimum Velocity at the Highest Point and at the Midway Point.
Concepts [12]
- Angular Displacement
- Angular Velocity
- Angular Acceleration
- Angular Velocity and Its Relation with Linear Velocity
- Uniform Circular Motion (UCM)
- Radial Acceleration
- Dynamics of Uniform Circular Motion - Centripetal Force
- Centrifugal Forces
- Banking of Roads
- Vertical Circular Motion Due to Earth’s Gravitation
- Equation for Velocity and Energy at Different Positions of Vertical Circular Motion
- Kinematical Equations for Circular Motion in Analogy with Linear Motion.
