# Angular Position, Velocity, and Accelration.

1. Oct 18, 2009

### bolivartech

1. The problem statement, all variables and given/known data

During a certain period of time, the angular position of a swinging door is described by θ = 5.00 + 10.0t + 2.00t2, where θ is in radians and t is in seconds. Determine the angular position, angular speed, and angular acceleration of the door (a) at t = 0 and (b) at t = 3.00 s.

2. Relevant equations

ω = dθ / dt

α = dω / dt

3. The attempt at a solution

a) θ = 5.00
ω = 5 / 0
α = dω / 0

This just doesn't make sense, you cannot divide by 0.

But the other formulas, have either both ω and α or t cancels everything out.

This is supposed to be a simple problem of instantaneous angular speed and acceleration, how am I over complicating this?

2. Oct 18, 2009

### cepheid

Staff Emeritus
The expressions dθ/dt and dω/dt are not fractions. They are derivatives. Have you studied calculus? Do you know what differentiation is (the process of taking a derivative)? I'm asking because your attempted solution suggests that you don't.

d/dt is a symbol which, when applied to function, means, "take the derivative of that function with respect to time."

In this case, the function is θ (or θ(t), to show the argument explicitly), and we write:

dθ/dt = d/dt (5.00 + 10.0t + 2.00t2 )

Now, knowing how to actually calculate the derivative of this function of time requires knowing differential calculus.

3. Oct 18, 2009

### bolivartech

Thanks, I don't know why I didn't see that.... I stayed up way to late working on homework I actually enjoy doing.

ω = dθ/dt = d/dt (5.00 + 10.0t + 2.00t2 ) = 10