Curvilinear Motion: Polar Coordinates (Engineering Dynamics)

[Andy907]

Homework Statement

Homework Equations

The Attempt at a Solution

I have stared at this for hours and don't know where to start. I think I need to get r in terms of t but I don't really know how with the information given. I just need a good hint to get started.

 

[Chestermiller]

In polar coordinates, what are the equations for the r and θ components of acceleration?

 

[Andy907]

In polar coordinates, what are the equations for the r and θ components of acceleration?

a = (Rdouble dot - Rθdot²)e_R + (Rθdouble dot + 2Rdotθdot)e_θ

I know a = 15 m/s². I also know that the dot means the derivative is taken in respect to time. That's where I'm drawing a blank and why I thought the given R equation had to be manipulated in some way to be in terms of t. Or possibly solve for θ in terms of t and then substitute that equation into θ in the original given R equation.

In all the examples we did in class θ was given in terms of t, so it was pretty simple to substitute that equation into the given r equation and then take the derivatives.

 

[Chestermiller]

From Eqn. 3.1, in terms of dθ/dt and θ, what is dr/dt?
What is $\frac{d^2r}{dt^2}$ in terms of θ, dθ/dt, and d²θ/dt².