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A wheel of moment of inertia 0.40 kg-m2 is making 2100 rotations per minute. The wheel is brought to a complete stop in 2 seconds. The angular acceleration of the wheel is
- a)35π radians/second2
- b)110π radians/second2
- c)55π radians/second2
- d)220π radians/second2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A wheel of moment of inertia 0.40 kg-m2 is making 2100 rotations per m...
CONCEPT:
- Angular velocity (ω): How fast the angular position or orientation of an object changes with time or How fast an object rotates or revolves relative to another point is known as angular velocity.
- Angular velocity in terms of RPM (revolutions per minute)
ω = 2 π f / 60
where ω is in terms of radian per second and f is in revolution per minute.
- Angular acceleration (α): The rate of change of angular velocity is known as angular acceleration.
The relation between α and changing ω is given by:
ω1 = ω0 + α t
where ω1 is the final angular velocity, ω0 is the initial angular velocity α is the angular acceleration.
CALCULATION:
Given that f0 = 2100 rpm; f1 = 0 rpm; t = 2 sec.
ω0 = 2 π f0 / 60 = 2 π 2100 / 60 = 70π
ω1 = 0
ω1 = ω0 + α t
0 = 70π + α 2
α = -35π rad/sec2
So the correct answer is option 1.
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Community Answer
A wheel of moment of inertia 0.40 kg-m2 is making 2100 rotations per m...
Given Data
- Moment of Inertia (I) = 0.40 kg-m²
- Initial rotational speed (ω₀) = 2100 rotations/minute
- Time to stop (t) = 2 seconds
Convert Rotational Speed
- Rotational speed in radians per second:
- 1 rotation = 2π radians
- ω₀ = 2100 rotations/minute × (2π radians/rotation) × (1 minute/60 seconds)
- ω₀ = 2100 × (2π/60) = 220π radians/second
Final Rotational Speed
- Final speed (ω) = 0 radians/second (since it comes to a stop)
Calculate Angular Acceleration
- Angular acceleration (α) can be calculated using the formula:
- α = (ω - ω₀) / t
- Substitute the values:
- α = (0 - 220π) / 2
- α = -220π / 2
- α = -110π radians/second²
Direction of Angular Acceleration
- The negative sign indicates that the angular acceleration is acting in the opposite direction to the rotation, which is expected as the wheel is coming to a stop.
Final Answer
- The magnitude of angular acceleration is:
- α = 110π radians/second²
However, since the correct answer is option 'A', it seems there might be a misunderstanding in the interpretation of the options. The answer α = 110π radians/second² aligns with the calculation but is not listed as the correct option. The question may have intended for the absolute value or a misunderstanding in the labeling of options. Please verify the options provided in the question to ensure consistency.
- Moment of Inertia (I) = 0.40 kg-m²
- Initial rotational speed (ω₀) = 2100 rotations/minute
- Time to stop (t) = 2 seconds
Convert Rotational Speed
- Rotational speed in radians per second:
- 1 rotation = 2π radians
- ω₀ = 2100 rotations/minute × (2π radians/rotation) × (1 minute/60 seconds)
- ω₀ = 2100 × (2π/60) = 220π radians/second
Final Rotational Speed
- Final speed (ω) = 0 radians/second (since it comes to a stop)
Calculate Angular Acceleration
- Angular acceleration (α) can be calculated using the formula:
- α = (ω - ω₀) / t
- Substitute the values:
- α = (0 - 220π) / 2
- α = -220π / 2
- α = -110π radians/second²
Direction of Angular Acceleration
- The negative sign indicates that the angular acceleration is acting in the opposite direction to the rotation, which is expected as the wheel is coming to a stop.
Final Answer
- The magnitude of angular acceleration is:
- α = 110π radians/second²
However, since the correct answer is option 'A', it seems there might be a misunderstanding in the interpretation of the options. The answer α = 110π radians/second² aligns with the calculation but is not listed as the correct option. The question may have intended for the absolute value or a misunderstanding in the labeling of options. Please verify the options provided in the question to ensure consistency.
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A wheel of moment of inertia 0.40 kg-m2 is making 2100 rotations per minute. The wheel is brought to a complete stop in 2 seconds. The angular acceleration of the wheel isa)35π radians/second2b)110π radians/second2c)55π radians/second2d)220π radians/second2Correct answer is option 'A'. Can you explain this answer?
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