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?
Practice Questions
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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?
θ = αt²
θ = 0.5αt²
θ = αt
θ = 0.5αt
Angular displacement θ = 0.5αt² for constant angular acceleration.
Questions & Step-by-step Solutions
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Q
Q: 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?
Solution: Angular displacement θ = 0.5αt² for constant angular acceleration.
Steps: 6
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.
