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A wheel has a constant angular acceleration of 2 rad/second square, during a certain 4.0s interval ,it turns through an angle of 72 rad . assuming that at t-0, angular speed -6 rad /sec how long,is motion at the start of this 4.0 second interval ?
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A wheel has a constant angular acceleration of 2 rad/second square, du...
Given data:
Angular acceleration (α) = 2 rad/s²
Angle turned (θ) = 72 rad
Initial angular speed (ω₀) = -6 rad/s
Time interval (t) = 4.0 s

Calculating the time at the start of the interval:
To find the time at the start of the interval, we need to use the kinematic equation for rotational motion:

θ = ω₀t + (1/2)αt²

Step 1: Calculate the final angular speed (ω):
Using the formula:

ω = ω₀ + αt

Substituting the given values:

ω = -6 + 2(4.0) = -6 + 8 = 2 rad/s

Step 2: Rearrange the kinematic equation:
θ = ω₀t + (1/2)αt²

Rearranging the equation, we get:

(1/2)αt² + ω₀t - θ = 0

Step 3: Solve the quadratic equation:
Using the quadratic formula:

t = (-b ± √(b² - 4ac)) / (2a)

Where:
a = (1/2)α = α/2
b = ω₀
c = -θ

Substituting the values, we get:

t = (-(ω₀) ± √((ω₀)² - 4(a)(c))) / (2(a))

Plugging in the values:

t = (-(2) ± √((2)² - 4(α/2)(-72))) / (2(α/2))

Simplifying further:

t = (-2 ± √(4 + 8α)) / α

Step 4: Calculate the time at the start of the interval:
Using the positive value of the quadratic equation to represent time, we have:

t = (-2 + √(4 + 8α)) / α

Substituting the given value of α:

t = (-2 + √(4 + 8(2))) / 2

Simplifying further:

t = (-2 + √(4 + 16)) / 2

t = (-2 + √20) / 2

t = (-2 + 2√5) / 2

t = -1 + √5

Hence, the motion at the start of this 4.0 second interval is approximately equal to -1 + √5 seconds.
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A wheel has a constant angular acceleration of 2 rad/second square, during a certain 4.0s interval ,it turns through an angle of 72 rad . assuming that at t-0, angular speed -6 rad /sec how long,is motion at the start of this 4.0 second interval ?
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A wheel has a constant angular acceleration of 2 rad/second square, during a certain 4.0s interval ,it turns through an angle of 72 rad . assuming that at t-0, angular speed -6 rad /sec how long,is motion at the start of this 4.0 second interval ? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A wheel has a constant angular acceleration of 2 rad/second square, during a certain 4.0s interval ,it turns through an angle of 72 rad . assuming that at t-0, angular speed -6 rad /sec how long,is motion at the start of this 4.0 second interval ? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wheel has a constant angular acceleration of 2 rad/second square, during a certain 4.0s interval ,it turns through an angle of 72 rad . assuming that at t-0, angular speed -6 rad /sec how long,is motion at the start of this 4.0 second interval ?.
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