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Standard XII

Physics

a-t Graph

An object is ...

Question

An object is found to rotate with an angular velocity $ω (t) = 15 t^{2} - 30 t + 25$ , where $ω$ is measured in radians per second.
Which of the following best represents the time interval in which the angular acceleration of the object zero?

0.5 s

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1.0 s

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1.5 s

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2.0 s

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2.5 s

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Solution

The correct option is C $1.0 s$

Angular velocity of the object $w (t) = 15 t^{2} - 30 t + 25$ rad/s
Differentiating w.r.t time we get angular acceleration $α = \frac{d w (t)}{d t} = 30 t - 30$ $r a d / s^{2}$
According to question $α = 0$
$∴$ $30 t - 30 = 0$ $⟹$ $t = 1.0$ s

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An object is found to rotate with an angular velocity ω(t)=15t2−30t+25, where ω is measured in radians per second.Which of the following best represents the time interval in which the angular acceleration of the object zero?

The correct option is C 1.0sAngular velocity of the object w(t)=15t2−30t+25 rad/sDifferentiating w.r.t time we get angular acceleration α=dw(t)dt=30t−30 rad/s2According to question α=0∴ 30t−30=0 ⟹ t=1.0 s

An object is found to rotate with an angular velocity $ω (t) = 15 t^{2} - 30 t + 25$ , where $ω$ is measured in radians per second.
Which of the following best represents the time interval in which the angular acceleration of the object zero?

The correct option is C $1.0 s$

Angular velocity of the object $w (t) = 15 t^{2} - 30 t + 25$ rad/s
Differentiating w.r.t time we get angular acceleration $α = \frac{d w (t)}{d t} = 30 t - 30$ $r a d / s^{2}$
According to question $α = 0$
$∴$ $30 t - 30 = 0$ $⟹$ $t = 1.0$ s