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An object travels around a circle of radius r with constant speed. If s is the distance traveled in time t around the circle and theta is the central angle​ (in radians) swept out in time​ t, then the linear speed of the object is vequals​_____ and the angular speed of the object is omegaequals​______.

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lublana

Answer with Step-by-step explanation:

We are given that

Radius of circle=r

Total distance traveled =s

Time=t

Central angle=[tex]\theta[/tex] rad

We know that

Linear speed,v=[tex]\frac{distance}{time}[/tex]

Using the formula

Therefore, v=[tex]\frac{s}{t}[/tex]

Angular speed,[tex]\omega=\frac{Angular\;displacement}{time}[/tex]

By using the formula

[tex]\omega=\frac{\theta}{t}[/tex] rad/s

boffeemadrid

The linear speed and angular speed is required.

The linear speed is [tex]v=\dfrac{\theta r}{t}[/tex]

The angular speed is [tex]\omega=\dfrac{\theta}{t}[/tex]

[tex]\theta[/tex] = Angle in radians

[tex]t[/tex] = Time

[tex]r[/tex] = Radius

Linear Velocity is given by

[tex]v=\dfrac{\text{Distance}}{\text{Time}}[/tex]

Here the distance will be the arc length

[tex]\text{Distance}=\theta r[/tex]

So,

[tex]v=\dfrac{\theta r}{t}[/tex]

Linear velocity can also be written as

[tex]v=\dfrac{\theta}{t}r\\\Rightarrow v=\omega r[/tex]

So, [tex]\omega=\dfrac{\theta}{t}[/tex]

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https://brainly.com/question/2541917?referrer=searchResults

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