My Learning Cart
?
Categories
Account

A particle moves in a circular path of radius r with a constant angular accelera

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: A particle moves in a circular path of radius r with a constant angular acceleration α. What is the expression for the angular displacement θ after time t?

Options:

  1. θ = αt²
  2. θ = 0.5αt²
  3. θ = αt
  4. θ = 0.5αt

Correct Answer: θ = 0.5αt²

Solution: 

Angular displacement θ = 0.5αt² for constant angular acceleration.

A particle moves in a circular path of radius r with a constant angular accelera

Practice Questions

Q1
A particle moves in a circular path of radius r with a constant angular acceleration α. What is the expression for the angular displacement θ after time t?
  1. θ = αt²
  2. θ = 0.5αt²
  3. θ = αt
  4. θ = 0.5αt

Questions & Step-by-Step Solutions

A particle moves in a circular path of radius r with a constant angular acceleration α. What is the expression for the angular displacement θ after time t?
  • Step 1: Understand that angular displacement (θ) is how much the particle has rotated around the circle.
  • Step 2: Recognize that when a particle moves with constant angular acceleration (α), its speed changes at a constant rate.
  • Step 3: Recall the formula for angular displacement under constant angular acceleration, which is θ = θ₀ + ω₀t + 0.5αt², where θ₀ is the initial angular displacement and ω₀ is the initial angular velocity.
  • Step 4: If the particle starts from rest, then the initial angular velocity (ω₀) is 0 and the initial angular displacement (θ₀) is also 0.
  • Step 5: Substitute ω₀ = 0 and θ₀ = 0 into the formula, simplifying it to θ = 0.5αt².
  • Step 6: Conclude that the expression for angular displacement θ after time t with constant angular acceleration α is θ = 0.5αt².
  • Angular Motion – The study of rotational motion, including concepts like angular displacement, angular velocity, and angular acceleration.
  • Constant Angular Acceleration – A condition where the angular acceleration remains constant over time, allowing for the use of kinematic equations for rotational motion.
  • Kinematic Equations for Rotation – Equations that relate angular displacement, angular velocity, angular acceleration, and time, similar to linear motion equations.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks