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A wheel rotates with the constant acceleration of 2.0 rad/s2, if the wheel starts from rest the number of revolution it makes in first ten seconds will be approximately
- a)32
- b)24
- c)16
- d)8
Correct answer is option 'C'. Can you explain this answer?
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To solve this problem, we can use the kinematic equations of rotational motion. The key equation we will use is:
θ = ω₀t + (1/2)αt²
where:
θ is the angle or displacement in radians,
ω₀ is the initial angular velocity in radians per second,
α is the angular acceleration in radians per second squared,
t is the time in seconds.
In this case, we are given that the wheel starts from rest, so the initial angular velocity is 0. We are also given that the angular acceleration is 2.0 rad/s² and the time is 10 seconds. We need to find the number of revolutions made by the wheel in this time period.
Let's solve the problem step by step:
1. Calculate the final angular velocity:
Using the equation ω = ω₀ + αt, we can find the final angular velocity:
ω = 0 + 2.0 * 10 = 20 rad/s
2. Calculate the angle or displacement:
Using the equation θ = ω₀t + (1/2)αt², we can find the angle:
θ = 0 + (1/2) * 2.0 * (10)² = 100 rad
3. Convert the angle to revolutions:
Since 1 revolution is equal to 2π radians, we can find the number of revolutions by dividing the angle by 2π:
Number of revolutions = θ / (2π) = 100 / (2π) ≈ 15.92
4. Round the answer to the nearest whole number:
Since the question asks for the approximate number of revolutions, we round the answer to the nearest whole number:
Number of revolutions ≈ 16
Therefore, the correct answer is option C: 16 revolutions.
θ = ω₀t + (1/2)αt²
where:
θ is the angle or displacement in radians,
ω₀ is the initial angular velocity in radians per second,
α is the angular acceleration in radians per second squared,
t is the time in seconds.
In this case, we are given that the wheel starts from rest, so the initial angular velocity is 0. We are also given that the angular acceleration is 2.0 rad/s² and the time is 10 seconds. We need to find the number of revolutions made by the wheel in this time period.
Let's solve the problem step by step:
1. Calculate the final angular velocity:
Using the equation ω = ω₀ + αt, we can find the final angular velocity:
ω = 0 + 2.0 * 10 = 20 rad/s
2. Calculate the angle or displacement:
Using the equation θ = ω₀t + (1/2)αt², we can find the angle:
θ = 0 + (1/2) * 2.0 * (10)² = 100 rad
3. Convert the angle to revolutions:
Since 1 revolution is equal to 2π radians, we can find the number of revolutions by dividing the angle by 2π:
Number of revolutions = θ / (2π) = 100 / (2π) ≈ 15.92
4. Round the answer to the nearest whole number:
Since the question asks for the approximate number of revolutions, we round the answer to the nearest whole number:
Number of revolutions ≈ 16
Therefore, the correct answer is option C: 16 revolutions.
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A wheel rotates with the constant acceleration of2.0rad/s2, if the wheel starts from rest the number of revolution it makes in first ten seconds will be approximatelya)32b)24c)16d)8Correct answer is option 'C'. Can you explain this answer?
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