Answer:
α = 2.6 +1.7 t - 0.14 t³
Explanation:
Given that
ω(t) = at + bt² - ct⁴
where a = 2.6 rad/s², b = 0.85 rad/s³ and c = 0.035 rad/s⁵
We know that angular acceleration is the rate of change of angular velocity
α = dω/dt
ω(t) = at + bt² - ct⁴
dω/dt= a + 2 b t - 4 ct³
So
α = a + 2 b t - 4 ct³
By putting the values of a b and c
α = a + 2 b t - 4 ct³
α = 2.6 + 2 x 0.85 t - 4 x 0.035 t³
α = 2.6 +1.7 t - 0.14 t³
Answer:
[tex]a(t)=a+2bt-4ct^{3}[/tex]
Explanation:
We have the following angular speed equation :
[tex]w(t)=at+bt^{2}-ct^{4}[/tex]
We also know the parameters :
[tex]a=2.6\frac{rad}{s^{2}}[/tex]
[tex]b=0.85\frac{rad}{s^{3}}[/tex]
[tex]c=0.035\frac{rad}{s^{5}}[/tex]
We need the equation of the angular acceleration in terms of a,b and c.
We know that the angular acceleration is the rate of change of angular speed respect time.
Therefore, to obtain the equation a(t) we need to derivate w(t) in respect of the variable t.
[tex]w(t)=at+bt^{2}-ct^{4}[/tex] ⇒ derivating in respect of t ⇒
[tex]a(t)=a+2bt-4ct^{3}[/tex]
And that is the angular acceleration equation in terms of a,b and c.
