Question

A disc of radius 10 cm is rotating about its axis at an angular speed of 20 rad/s. Find the linear speed of
(a) a point on the rim,
(b) the middle point of a radius.

Answer 1

Explanation:

given:

angular speed=20 rad/s

radius(r)=0.1 m

linear speed

(a)at a point on the rim=20*0.1= 2m/s

(b)the middle point of the radius=20*0.5= 1 m/s

Answer 2

The linear speed of

(a) a point on the rim,  is 2 m/s

(b) the middle point of a radius is  r' = 1 m/s.

Explanation:

In view of the principles in the problem ,    

ω is Angular speed,

                                ω = 20 rad/s

                                r = 10 cm  

Converting radius from centimeter to meter

                                $r=\frac{10}{100}=0.10 \mathrm{m}$

Where,   r  is A disc of radius

(a) A point on the rim,

Here, the linear speed at the rim = ωr

                                                      = 20 x 0.10

                                                      = 2 m/s

(b) The middle point of a radius :

The center of the radius,  

                                        $r^{\prime}=\frac{0.10}{2}$

                                      $r^{\prime}=0.05 \mathrm{m}$

Hence , the linear speed in the radius of the middle point = ωr'

                                         = 20 x 0.05

                                    r' = 1 m/s .