Calculus angular acceleration with respect to theta

[nick76342]

Homework Statement

A disk with a 0.4 m radius starts from rest and is given an angular acceleration α = (10θ^2/3)rad/s² , where θ is in radians. Determine the magnitude of the normal (centripetal and tangential components of a point P on the rim of the disk when t = 4s.

Homework Equations

α = dω/dt
ω = dθ/dt
V_t = ω * r
a_c = V_t²/r

The Attempt at a Solution

I have been successful in finding ω, but only in terms of θ. Our teacher has showed us a method by which we use the ω = dθ/dt equation to find θ, however the method that he used involved dividing θ through anti-derivatives. I am not sure how this works in terms of legal math. I see that this problem exists elsewhere so what is the conventional way of solving? My calculus II teacher was not pleased with my physic's teachers method of solving. Any ideas? I am able to solve for everything else in this problem, I just need to find theta from the equation I derived (which I know is correct) ω = (√(15) * θ^2/3)rad/s.Thanks.

 

[Orodruin]

You know that $\omega = d\theta/dt$. Inserting this into your expression gives yoy a separable differential equation.

 

[fresh_42]

Homework Statement

A disk with a 0.4 m radius starts from rest and is given an angular acceleration α = (10θ^2/3)rad/s² , where θ is in radians. Determine the magnitude of the normal (centripetal and tangential components of a point P on the rim of the disk when t = 4s.

Homework Equations

α = dω/dt
ω = dθ/dt
V_t = ω * r
a_c = V_t²/r

The Attempt at a Solution

I have been successful in finding ω, but only in terms of θ. Our teacher has showed us a method by which we use the ω = dθ/dt equation to find θ, however the method that he used involved dividing θ through anti-derivatives. I am not sure how this works in terms of legal math. I see that this problem exists elsewhere so what is the conventional way of solving? My calculus II teacher was not pleased with my physic's teachers method of solving. Any ideas? I am able to solve for everything else in this problem, I just need to find theta from the equation I derived (which I know is correct) ω = (√(15) * θ^2/3)rad/s.Thanks.

You marked the problem as solved. Can you show us your solution?