A rigid body rotates about a stationary axis according to the law -at-bt3- awhere a-6 rad s and b-2 rad s 3- Then mean value of angular velocity - over the interval t-0 and the moment when it comes to rest is-

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Standard XII

Mathematics

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A rigid body ...

Question

A rigid body rotates about a stationary axis according to the law $θ = a t - b t^{3}$ . awhere $a = 6 \frac{r a d}{s}$ and $b = 2 \frac{r a d}{s^{3}}$ . Then mean value of angular velocity $(ω)$ over the interval $t = 0$ and the moment when it comes to rest is:

4 r a d / s

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3 r a d / s

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8 r a d / s

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6 r a d / s

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Solution

The correct option is A $4 r a d / s$
$θ = a t - b t^{3}$
$ω = a - 3 b t^{2}$
when it comes to rest $ω = 0$
$t = 1 s$
mean value of angular velocity= $\frac{a t - b t^{3}}{t} = 6 - 2 = 4 r a d / s e c$

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A rigid body rotates about a stationary axis according to the law θ=at−bt3. awhere a=6rads and b=2rads3. Then mean value of angular velocity (ω) over the interval t=0 and the moment when it comes to rest is:

The correct option is A 4 rad/sθ=at−bt3ω=a−3bt2when it comes to rest ω=0t=1smean value of angular velocity=at−bt3t=6−2=4rad/sec

A rigid body rotates about a stationary axis according to the law $θ = a t - b t^{3}$ . awhere $a = 6 \frac{r a d}{s}$ and $b = 2 \frac{r a d}{s^{3}}$ . Then mean value of angular velocity $(ω)$ over the interval $t = 0$ and the moment when it comes to rest is:

The correct option is A $4 r a d / s$
$θ = a t - b t^{3}$
$ω = a - 3 b t^{2}$
when it comes to rest $ω = 0$
$t = 1 s$
mean value of angular velocity= $\frac{a t - b t^{3}}{t} = 6 - 2 = 4 r a d / s e c$