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A wheel has an angular acceleration of 4 rad/s². If it starts from rest, how many revolutions will it complete in 10 seconds?
- a)10 revolutions
- b)20 revolutions
- c)40 revolutions
- d)200 revolutions
Correct answer is option 'D'. Can you explain this answer?
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A wheel has an angular acceleration of 4 rad/s². If it starts fro...
The angular acceleration of a wheel is given as 4 rad/s. This means that the wheel's rotational speed is increasing by 4 radians per second every second.
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A wheel has an angular acceleration of 4 rad/s². If it starts fro...
The number of revolutions (N) completed by a wheel can be calculated using the formula:
N = (ω₀t + (1/2)αt²) / (2π)
N = (ω₀t + (1/2)αt²) / (2π)
where:
ω₀ = initial angular velocity (0 rad/s, as the wheel starts from rest),
t = time, and
α = angular acceleration.
ω₀ = initial angular velocity (0 rad/s, as the wheel starts from rest),
t = time, and
α = angular acceleration.
Simplifying the formula for the given scenario:
N = (1/2)αt² / (2π)
N = (1/2)αt² / (2π)
Substituting the given values:
N = (1/2) * 4 rad/s² * (10 s)² / (2π)
N = 80 revolutions
N = (1/2) * 4 rad/s² * (10 s)² / (2π)
N = 80 revolutions
Therefore, the wheel will complete 80 revolutions in 10 seconds.
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A wheel has an angular acceleration of 4 rad/s². If it starts from rest, how many revolutions will it complete in 10 seconds?a)10 revolutionsb)20 revolutionsc)40 revolutionsd)200 revolutionsCorrect answer is option 'D'. Can you explain this answer?
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