Question

Derive the relation between Omega and speed at time t. And also solve this
If a particle is moving in a circular path with speed 10 metre per second if the radius of the circle is 2 metre then find out its angular speed
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Answer 1

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$\bold{Relationship \: between} \\ \bold{(\vec{W}) \: and \: (\vec{Vt})}$

We know that

$\boxed{ \delta{Q} = \frac{ \delta{S}}{r}}$

$= > \delta{S} = \delta{Q} \times r$

On Dividing with 't'

$= > \frac{ \delta{S}}{t} = (r) \times \frac{ (\delta{Q})}{t} \\ = > \boxed{Vt = (r) \times W} \\ \bold{or} \\ = > \boxed{V = r \times W} \\ \bold{As} \: \boxed{W = \frac{Q}{t} }$

It can also be written in Scalar form

$\boxed{\vec{V} = \vec{W} \times \vec{r}}$

Where,

$\vec{W} = Angular \: Velocity \\ \vec{V} = Tangential \: Velocity \\ \vec{r} = Radius \: Vector$

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Solution;

Given

V = 10 m/s

r = 2m

To find

W = ?????

We know that

$\boxed{V = r \times W}$

On putting Values

$= > 10 = r \times W \\ = > W = \frac{ \cancel10}{ \cancel2} \\ = > \huge \boxed{W = 5 \: rad/sec}$

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Answer 2

Answer:

5

Explanation:

Angular speed has a magnitude

(a value) only.

Angular speed = (final angle) - (initial angle) / time

= change in position/time.

ω = θ /t. ω = angular speed in radians/sec. θ = angle in radians (2π radians = 360 degrees)

w= 10/2

w= 5