how to find tangential acceleration

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How to find tangential and normal acceleration?

Thread starter reslion
Start date Jan 31, 2017
Tags

acceleration mechanics normal radial

Homework Statement

The problem asks for the tangential and normal acceleration of the acceleration. We were given that:
$$a_x=c*cos[d*t]$$ and $$a_y=c*sin[d*t]$$ where c and d are constants.

Homework Equations

The book gives us
$$a_t=(r\ddot{\theta}+2\dot{r}\dot{\theta})$$, (1)
$$a_n=(\ddot{r}-r\dot{\theta}^2$$ (2)
and
$$a=\sqrt{(a_t)^2+(a_n)^2}$$ (3)
but I found online that
$$a_t=\frac{dv}{dt}|v|$$ (4).
Finally, I know that $$a=\sqrt{(a_x)^2+(a_y)^2}$$ (5).

The Attempt at a Solution

My attempt was to use equation (4) as we don't have a theta to find $$a_{tx}$$ and $$a_{ty}$$. But wouldn't that just be the given accelerations as we would integrate the acceleration just to take the derivative again?
After that I would just solve (3) for $$a_n$$ of x and y and then plug both it in the (5) to find the magnitude of both $$a_t$$ and $$a_n$$. But I'm confused on how to find the tangential with either (1) or (4)?

Answers and Replies

I don't understand your equation 3. A correct version of that would be useful.
Remember that the tangential acceleration is, by definition, the component of the acceleration in the direction of the velocity.

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