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A wheel is subjected to uniform angular a cceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle q1 ; in the next 2 sec, it rotates through an additional angle q2. The ratio of q2 / q1 is-
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A wheel is subjected to uniform angular a cceleration about its axis. ...
From the second equation of motion we get that
Q1 = 0 + ½ a x 4
Where a is constant angular acceleration
Thus Q1 = 2a
Similarly Q2 = 0 + ½ x a x 16
Thus Q2 = 8a
We get Q2 / Q1 = 4
Q1 = 0 + ½ a x 4
Where a is constant angular acceleration
Thus Q1 = 2a
Similarly Q2 = 0 + ½ x a x 16
Thus Q2 = 8a
We get Q2 / Q1 = 4
Most Upvoted Answer
A wheel is subjected to uniform angular a cceleration about its axis. ...
Given:
Initial angular velocity, ω0 = 0
Time for first rotation, t1 = 2 s
Angle rotated in t1, q1
Time for second rotation, t2 = 2 s
Angle rotated in t2, q2
To find: q2/q1
Concept:
The angular displacement (q) of a rotating body with uniform angular acceleration (α) in time (t) is given by:
q = ω0t + 1/2 αt^2
where ω0 is the initial angular velocity.
Explanation:
For the first rotation:
The initial angular velocity, ω0 = 0
Angular acceleration, α = ?
Time, t1 = 2 s
Angular displacement, q1 = ?
Using the formula, q1 = ω0t1 + 1/2 αt1^2
q1 = 1/2 α(2)^2
q1 = 2α
For the second rotation:
The initial angular velocity, ω0 = 0
Angular acceleration, α = ?
Time, t2 = 2 s
Angular displacement, q2 = ?
Using the formula, q2 = ω0t2 + 1/2 αt2^2
q2 = 1/2 α(2)^2 + ω1t2
q2 = 2α + ω1t2
We know that, ω1 = ω0 + αt1
ω1 = α(2)
Substituting the value of ω1 in the above equation, we get:
q2 = 2α + 2α
q2 = 4α
Therefore, q2/q1 = 4α/2α = 2
Hence, the correct option is (C) 4.
Initial angular velocity, ω0 = 0
Time for first rotation, t1 = 2 s
Angle rotated in t1, q1
Time for second rotation, t2 = 2 s
Angle rotated in t2, q2
To find: q2/q1
Concept:
The angular displacement (q) of a rotating body with uniform angular acceleration (α) in time (t) is given by:
q = ω0t + 1/2 αt^2
where ω0 is the initial angular velocity.
Explanation:
For the first rotation:
The initial angular velocity, ω0 = 0
Angular acceleration, α = ?
Time, t1 = 2 s
Angular displacement, q1 = ?
Using the formula, q1 = ω0t1 + 1/2 αt1^2
q1 = 1/2 α(2)^2
q1 = 2α
For the second rotation:
The initial angular velocity, ω0 = 0
Angular acceleration, α = ?
Time, t2 = 2 s
Angular displacement, q2 = ?
Using the formula, q2 = ω0t2 + 1/2 αt2^2
q2 = 1/2 α(2)^2 + ω1t2
q2 = 2α + ω1t2
We know that, ω1 = ω0 + αt1
ω1 = α(2)
Substituting the value of ω1 in the above equation, we get:
q2 = 2α + 2α
q2 = 4α
Therefore, q2/q1 = 4α/2α = 2
Hence, the correct option is (C) 4.
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A wheel is subjected to uniform angular a cceleration about its axis. ...
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A wheel is subjected to uniform angular a cceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle q1; in the next 2 sec, it rotates through an additional angle q2. The ratio of q2/ q1is-a)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer?
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