Question

As steam is slowly injected into a turbine, the angular acceleration of the rotor is observed to increase linearly with the time t. Know that the rotor starts from rest at t = 0 and that after 10 s the rotor has completed 20 revolutions.Choose the correct equations of motion for the rotor. (You must provide an answer before moving on to the next part.)

a) a = 2kt, w = 3krº, and 8 = 4kr
b) a = {kt, w = ke?, and 0 = }ke?
c) a = kr?, w = jke', and 0 = krº
d) a = kt, w = jke?, and 0 kr

Answer 1

α = kt

ω =
`(kt^2)/(2)`

θ =
`(kt^3)/(6)`

Step-by-step explanation:

given data

Initial velocity ω = 0

time t = 10 s

Number of revolutions = 20

solution

we will take here first α = kt .....................1

and as α =
`(d\omega)/(dt)`

so that

`(d\omega)/(dt)` = kt ..................2

now we will integrate it then we will get

∫dω =
`\int_(0)^(t) kt\ dt` .......................3

so

ω =
`(kt^2)/(2)`

and

ω =
`(d\theta)/(dt)` ..............4

so that

`(d\theta)/(dt)` =
`(kt^2)/(2)`

now we will integrate it then we will get

∫dθ =
`\int_(0)^(t)(kt^2)/(2) \ dt` ...............5

solve it and we get

θ =
`(kt^3)/(6)`