Relative Velocity and Uniform Circular Motion
Relative motion in one and two dimensions and centripetal acceleration. (Physics › Kinematics, NEET UG syllabus.)
What is Relative Velocity and Uniform Circular Motion?
The velocity of an object with respect to another object or a different frame of reference.
Key formula / rule: Relative Velocity (1D)
Key points
- Define and calculate relative velocity in one and two dimensions.
- Understand the concept of a frame of reference.
- Describe Uniform Circular Motion and its characteristics.
- Explain the origin and direction of centripetal acceleration.
Common exam trap
Incorrectly applying vector subtraction for relative velocity in 2D (e.g., scalar subtraction).
Definitions
- Term
Relative Velocity
- Meaning
The velocity of an object with respect to another object or a different frame of reference.
- Term
Uniform Circular Motion (UCM)
- Meaning
The motion of an object moving at a constant speed along a circular path.
- Term
Centripetal Acceleration
- Meaning
The acceleration directed towards the center of a circular path, responsible for changing the direction of velocity in UCM.
- Term
Angular Velocity (ω)
- Meaning
The rate of change of angular displacement, measured in radians per second (rad/s).
- Term
Time Period (T)
- Meaning
The time taken for one complete revolution in circular motion.
- Term
Frequency (f)
- Meaning
The number of revolutions per second in circular motion.
Learning objectives
Define and calculate relative velocity in one and two dimensions.
Understand the concept of a frame of reference.
Describe Uniform Circular Motion and its characteristics.
Explain the origin and direction of centripetal acceleration.
Derive and apply formulae for centripetal acceleration.
Relate linear velocity, angular velocity, time period, and frequency in UCM.
Solve problems involving relative motion and uniform circular motion.
Formulae
- Name
Relative Velocity (1D)
- Note
For objects A and B moving in 1 dimension. Sign convention is crucial.
- Expression
vAB = vA - vB
- Name
Relative Velocity (2D)
- Note
Vector subtraction for objects A and B moving in 2 dimensions.
- Expression
vec(v)AB = vec(v)A - vec(v)B
- Name
Relation between Linear and Angular Velocity
- Note
Where v is tangential speed, r is radius, ω is angular velocity.
- Expression
v = rω
- Name
Centripetal Acceleration (using linear speed)
- Note
Acceleration directed towards the center of the circular path.
- Expression
ac = v2/r
- Name
Centripetal Acceleration (using angular velocity)
- Note
Acceleration directed towards the center of the circular path.
- Expression
ac = ω2r
- Name
Time Period (T)
- Note
Time for one complete revolution.
- Expression
T = 2π/ω
- Name
Frequency (f)
- Note
Number of revolutions per second.
- Expression
f = 1/T = ω/(2π)
Prerequisites
Basic concepts of displacement, velocity, and acceleration.
Vector addition and subtraction (graphical and analytical methods).
Resolution of vectors into components.
Basic trigonometry.
Common mistakes
Incorrectly applying vector subtraction for relative velocity in 2D (e.g., scalar subtraction).
Forgetting to assign correct signs for velocities in 1D relative motion problems.
Confusing centripetal acceleration with tangential acceleration.
Assuming zero acceleration in UCM because speed is constant.
Using degrees instead of radians for angular displacement or velocity calculations.
Incorrectly relating linear and angular quantities (e.g., v = ω/r instead of v = rω).
Keywords
Relative velocity
Frame of reference
Uniform Circular Motion
Centripetal acceleration
Angular velocity
Time period
Frequency
Tangential velocity
Vector subtraction
Practice preview
A car A is moving with a velocity of 20 m/s towards East and another car B is moving with a velocity of 15 m/s towards East. What is the relative velocity of car A with respect to car B?…
easy
A boat can travel with a speed of 5 km/h in still water. If the river flows with a speed of 3 km/h, what is the minimum time taken by the boat to cross a river of width 4 km?…
medium
Which of the following statements is INCORRECT regarding a particle undergoing circular motion?…
hard