- #1

arhzz

- 266

- 52

- Homework Statement
- The angular speed of a turbine with a diameter of d = 1m increases steadily from 20rad / s to 40rad / s within 4s.

a) Calculate the angular acceleration

b) the total angle that the turbine has rotated during this time interval.

c) What is the normal acceleration that acts on the outermost tip of the turbine blade at the top speed?

- Relevant Equations
- a(t) = w/t

Okay so what I've done;

I've put the diammter d = 1m as r = 1m

The time interval of 4s is t = 4s

and the angular velocitys as;

ω1 = 20 rad/s

ω2 = 40 rad/s

Now to get the accelaration. Angular acceleration can be split into two parts tangetial acceleration and radial acceleration

What I think is what I am looking in this example (under a) is the radial acceleration.

I've found this formula to get angular acceleration

$$ a = \frac { \Delta \omega}{\Delta t} $$So for ## \Delta \omega ## I've done this

$$ \Delta \omega = \omega 2 - \omega 1 $$

That should be 20 rad/s, as for ## \Delta t## I'd reckon it remains 4, because 4 - 0 is 4

So a should be

$$ a = \frac {40 - 20} {4} $$

$$ a = 5 \frac {rad} {s^2} $$Now the problem is that although the unit should be rad/s^2 when I input the unit of omega and time in the calculation I'dont get rad/s^2,which means that my calculation is probably wrong. Could anyone confirm my thought process ? And if it is wrong what would be a good starting point, thank you!

I've put the diammter d = 1m as r = 1m

The time interval of 4s is t = 4s

and the angular velocitys as;

ω1 = 20 rad/s

ω2 = 40 rad/s

Now to get the accelaration. Angular acceleration can be split into two parts tangetial acceleration and radial acceleration

What I think is what I am looking in this example (under a) is the radial acceleration.

I've found this formula to get angular acceleration

$$ a = \frac { \Delta \omega}{\Delta t} $$So for ## \Delta \omega ## I've done this

$$ \Delta \omega = \omega 2 - \omega 1 $$

That should be 20 rad/s, as for ## \Delta t## I'd reckon it remains 4, because 4 - 0 is 4

So a should be

$$ a = \frac {40 - 20} {4} $$

$$ a = 5 \frac {rad} {s^2} $$Now the problem is that although the unit should be rad/s^2 when I input the unit of omega and time in the calculation I'dont get rad/s^2,which means that my calculation is probably wrong. Could anyone confirm my thought process ? And if it is wrong what would be a good starting point, thank you!