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Standard XII

Physics

Pseudo Force

A wheel rotat...

Question

A wheel rotates so that the angle of rotation is proportional to the square of the time. The first revolution was performed by the wheel for $8$ seconds the angular velocity at this time is

π r a d / s e c

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2 π r a d / s e c

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\frac{π}{2} r a d / s e c

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\frac{π}{3} r a d / s e c

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Solution

The correct option is A $π r a d / s e c$
Given, $θ a t^{2}$
Here $θ$ is angle of rotation $t$ is time
By formula, $θ = \frac{1}{2} α t^{2}$
At $t = 8,$ one rotation is done
So, $2 π = \frac{1}{2} \times α \times (8)^{2}$
$4 π = 64 α$
$π / 46 = α$
$w = 2 \times \frac{π}{16} \times 8$
$w = π r a d / s$ .
Thus, angular velocity is $π r a d / s$

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Similar questions

A wheel rotates so that the angle of rotation is proportional to the square of time. The first revolution was performed by the wheel for 8 sec. Find the angular velocity 32 sec after the wheel started.

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The wheel started from rest is uniformly accelerated with alpha = 4 rad/second Square for 10 sec. It is then allowed to rotate uniformly for next 2 sec & is finally brought to rest in the next 10 sec . Find the total angle rotated by the wheel .

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A wheel rotates so that the angle of rotation is proportional to the square of the time. The first revolution was performed by the wheel for 8 seconds the angular velocity at this time is

The correct option is A π rad/secGiven, θat2Here θ is angle of rotation t is timeBy formula, θ=12αt2At t=8, one rotation is done So, 2π=12×α×(8)24π=64απ/46=αw=2×π16×8w=π rad/s.Thus, angular velocity is π rad/s

A wheel rotates so that the angle of rotation is proportional to the square of the time. The first revolution was performed by the wheel for $8$ seconds the angular velocity at this time is