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A ball moving with angular velocity of 2 π/s is made to stop in 50 seconds. what is the angular acceleration of the ball?
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A ball moving with angular velocity of 2 π/s is made to stop in 50 sec...
To determine the angular acceleration of a ball that is brought to a stop, we can apply the formula for angular acceleration, which relates initial angular velocity, final angular velocity, time, and angular acceleration.
Given Data
- Initial angular velocity (ω₀): 2 π/s
- Final angular velocity (ω): 0 (since the ball stops)
- Time (t): 50 seconds
Formula for Angular Acceleration
The angular acceleration (α) can be calculated using the formula:
α = (ω - ω₀) / t
Substituting the values:
Calculating Angular Acceleration
- ω = 0 (final angular velocity)
- ω₀ = 2 π/s (initial angular velocity)
- t = 50 s (time taken to stop)
- α = (0 - 2 π) / 50
- α = -2 π / 50
- α = -π / 25 s²
Interpretation of Results
- The negative sign indicates that the angular velocity is decreasing, confirming that the ball is decelerating.
- The magnitude of the angular acceleration is π / 25 s², representing how quickly the ball is slowing down.
Conclusion
- The angular acceleration of the ball is -π / 25 s².
- This value indicates the rate at which the ball is being decelerated to a stop over 50 seconds.
Given Data
- Initial angular velocity (ω₀): 2 π/s
- Final angular velocity (ω): 0 (since the ball stops)
- Time (t): 50 seconds
Formula for Angular Acceleration
The angular acceleration (α) can be calculated using the formula:
α = (ω - ω₀) / t
Substituting the values:
Calculating Angular Acceleration
- ω = 0 (final angular velocity)
- ω₀ = 2 π/s (initial angular velocity)
- t = 50 s (time taken to stop)
- α = (0 - 2 π) / 50
- α = -2 π / 50
- α = -π / 25 s²
Interpretation of Results
- The negative sign indicates that the angular velocity is decreasing, confirming that the ball is decelerating.
- The magnitude of the angular acceleration is π / 25 s², representing how quickly the ball is slowing down.
Conclusion
- The angular acceleration of the ball is -π / 25 s².
- This value indicates the rate at which the ball is being decelerated to a stop over 50 seconds.
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A ball moving with angular velocity of 2 π/s is made to stop in 50 seconds. what is the angular acceleration of the ball?
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A ball moving with angular velocity of 2 π/s is made to stop in 50 seconds. what is the angular acceleration of the ball? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A ball moving with angular velocity of 2 π/s is made to stop in 50 seconds. what is the angular acceleration of the ball? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball moving with angular velocity of 2 π/s is made to stop in 50 seconds. what is the angular acceleration of the ball?.
A ball moving with angular velocity of 2 π/s is made to stop in 50 seconds. what is the angular acceleration of the ball? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A ball moving with angular velocity of 2 π/s is made to stop in 50 seconds. what is the angular acceleration of the ball? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball moving with angular velocity of 2 π/s is made to stop in 50 seconds. what is the angular acceleration of the ball?.
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