Homework Help: Problem resolving forces into components

1. Sep 22, 2014

yugeci

I have problems with this question:

This is how I resolved v into its components (Vr and Vtheta):

So with this I get
Vr = - V cos theta
Vtheta = V sin theta

However in my solution booklet the components are the other way around (Vr = - V sin theta, Vtheta = V cos theta) and I cannot figure out why. It makes no sense... am I right and the solution wrong?

2. Sep 22, 2014

Khashishi

The solution manual is wrong.

3. Sep 23, 2014

FactChecker

The extreme cases support you. When theta is small, (the piston is in line with the lever) almost all the change is in r and theta is almost constant. Conversely, when the lever arm is straight up (theta=90), r doesn't change and theta is the only thing changing. That puts the cos and sin where you have them.

4. Sep 23, 2014

yugeci

Thought so. Thanks. Another problem I have with the solution manual is that it says the magnitude of the total acceleration is zero and therefore the radial acceleration = angular acceleration (Ar = Atheta). Is this true? Because I thought the constant velocity only meant the tangential acceleration was zero... and there would be still be a normal acceleration equal to v^2 / r.

5. Sep 23, 2014

Khashishi

Either the solution manual is wrong again, or you have misread it somehow. $\ddot r$ and $\ddot theta$ have different units, so they can't be equal unless 0.