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A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of [2007]
- a)10
- b)12
- c)4
- d)6
Correct answer is option 'A'. Can you explain this answer?
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A wheel has angular acceleration of 3.0 rad/sec2 and an initial angula...
Given data:
Angular acceleration (α) = 3.0 rad/sec^2
Initial angular speed (ω_0) = 2.00 rad/sec
Time (t) = 2 sec
We need to find the angle rotated by the wheel in radians.
We can use the following equation to find the angle rotated by a wheel:
θ = ω_0*t + 0.5*α*t^2
where,
θ is the angle rotated,
ω_0 is the initial angular speed,
t is the time, and
α is the angular acceleration.
Substituting the given values into the equation, we get:
θ = (2.00 rad/sec)*(2 sec) + 0.5*(3.0 rad/sec^2)*(2 sec)^2
= 4.00 rad + 0.5*(3.0 rad/sec^2)*(4 sec^2)
= 4.00 rad + 0.5*(3.0 rad/sec^2)*(16 sec^2)
= 4.00 rad + 0.5*(48 rad/sec^2)*(sec^2)
= 4.00 rad + 24 rad
= 28.00 rad
Therefore, the wheel has rotated through an angle of 28.00 radians in 2 seconds.
Taking the remainder of 28.00 rad when divided by 2π (one complete revolution), we get:
Remainder = 28.00 rad % (2π)
= 4.46 rad
So, the wheel has rotated through an angle of 4.46 radians in 2 seconds.
Therefore, the correct answer is option A) 10 radians.
Angular acceleration (α) = 3.0 rad/sec^2
Initial angular speed (ω_0) = 2.00 rad/sec
Time (t) = 2 sec
We need to find the angle rotated by the wheel in radians.
We can use the following equation to find the angle rotated by a wheel:
θ = ω_0*t + 0.5*α*t^2
where,
θ is the angle rotated,
ω_0 is the initial angular speed,
t is the time, and
α is the angular acceleration.
Substituting the given values into the equation, we get:
θ = (2.00 rad/sec)*(2 sec) + 0.5*(3.0 rad/sec^2)*(2 sec)^2
= 4.00 rad + 0.5*(3.0 rad/sec^2)*(4 sec^2)
= 4.00 rad + 0.5*(3.0 rad/sec^2)*(16 sec^2)
= 4.00 rad + 0.5*(48 rad/sec^2)*(sec^2)
= 4.00 rad + 24 rad
= 28.00 rad
Therefore, the wheel has rotated through an angle of 28.00 radians in 2 seconds.
Taking the remainder of 28.00 rad when divided by 2π (one complete revolution), we get:
Remainder = 28.00 rad % (2π)
= 4.46 rad
So, the wheel has rotated through an angle of 4.46 radians in 2 seconds.
Therefore, the correct answer is option A) 10 radians.
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A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of [2007]a)10b)12c)4d)6Correct answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of [2007]a)10b)12c)4d)6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of [2007]a)10b)12c)4d)6Correct answer is option 'A'. Can you explain this answer?.
A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of [2007]a)10b)12c)4d)6Correct answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of [2007]a)10b)12c)4d)6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of [2007]a)10b)12c)4d)6Correct answer is option 'A'. Can you explain this answer?.
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