Question

A wheel of radius 50 Cm having an angular speedof 5 rad s-1 have linear speed.
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Answer 1

Given:

Radius $=50cm$

Angular speed $=5rad/s$

To find:

Linear velocity of the wheel.

Explanation:

The change in angular displacement of a body with respect to the time is called as the angular velocity of the body.

Mathematically,  ω $=\frac{d\alpha }{dt}$  

The SI unit of angular speed is rad/s.

If we consider a body moving along a circular path, having a radius $R$ . Let's say, the distance covered by the body in time $t$ is $l$. Hence, the angle of the sector of distance $l$ will be lets say θ.

The relation between $l$ , $R$  and θ is given by

θ $=\frac{l}{R}$  

Hence, $l=R$ θ

Differentiating both sides with respect to time $t$, we get

$\frac{dl}{dt} =R$ $\frac{d0}{dt}$

We get,

$v=R$ω

Solution:

According to the question, we have

$R=50cm=0.5m$

ω$=5rad/s$

Therefore, we get

$v=0.5(5)$

$v=2.5m/s$

Final answer:

Hence, the linear velocity of the object will be 2.5 m/s.