Respuesta :
[tex]r_{a}[/tex] = distance of point "a" from center of disk = r
[tex]r_{}[/tex] = distance of point "b" from center of disk = r/5
[tex]w_{a}[/tex] = angular velocity of point "a"
[tex]w_{b}[/tex] = angular velocity of point "b"
[tex]v_{a}[/tex] = tangential velocity of point "a"
[tex]v_{b}[/tex] = tangential velocity of point "b"
We know that angular velocity is independent of the distance from the center, hence the angular velocity is same at all points on the disk.
[tex]w_{a}[/tex] = [tex]w_{b}[/tex]
Ratio of angular velocity = [tex]\frac{w_{a}}{w_{b}}[/tex]
Ratio of angular velocity = [tex]\frac{w_{b}}{w_{b}}[/tex]
Ratio of angular velocity = 1
Tangential velocity is given as
v = r w
hence the ratio of tangential velocity is given as
Ratio of tangential velocity = [tex]\frac{v_{a}}{v_{b}}[/tex]
Ratio of tangential velocity = [tex]\frac{r_{a}w_{a}}{r_{b}w_{b}}[/tex]
Ratio of tangential velocity = [tex]\frac{r w_{b}}{(r/5)w_{b}}[/tex]
Ratio of tangential velocity = 5
The given locations of a radial length and a 5th of the radial length gives;
- Ratio of the angular velocity at point a to point b is 1 : 1
- Ratio of the tangential velocity at point a to point b is 5 : 1
How can the ratio of the velocities be found?
The angular velocity is given by the equation;
[tex] \omega \: = \frac{angle \: turned}{time} = \frac{1}{ period} [/tex]
Where;
A period, T = The time to complete a cycle
The angle turned by point a and point b at the same time, t, are equal, therefore;
[tex] \omega a = \omega b[/tex]
Which gives;
[tex] \frac{ \omega a}{ \omega b} = \frac{ \omega a}{ \omega a} = 1[/tex]
The ratio of the angular velocity,
[tex]{ \omega a}[/tex] to the angular velocity [tex]{ \omega b}[/tex] is therefore;
[tex]{ \omega a}[/tex] : [tex]{ \omega b}[/tex] = 1 : 1
Similarly, we have;
Tangential velocity, va = v × r
Tangential velocity, vb = v × r/5
va/vb = 5/1
va:vb = 5 : 1
Learn more about angular (rotational) velocity here:
https://brainly.com/question/1452612
