How Do You Calculate the Velocity of a Swinging Mass?

[tcg]

There is an arm which is fixed at one end so the other can swing freely. At the other end there is a mass. Assuming the only force acting on the mass is gravity and it starts falling from, say, forty-five degrees from the horizontal, you must be able to figure out its velocity at any given point in its fall?

I know its acceleration at any point is g cos theta (measured from the horizontal) but I don't know how to integrate that sensibly to get a velocity.

If I integrate with respect to time do I get an angular velocity (rad/s) or a linear velocity (m/s) or what?

My g cos theta expression takes the angle into account, but it's not really angular acceleration, or is it?

Any help appreciated.

 

[ojs]

You always get velocity if you integrate acceleration (and angular velocity if you integrate angular acceleration).
Note here also that velocity is a vector quantity with both an horizontal and vertical component. Acceleration is also a vector quantity, that's why you use the cos and sin functions but is it good to divide acceleration into its components, how would the orientation of those components be compared to the ground? How does that help you to find the velocity? Could you perhaps use normal kinematic equations to solve this problem and skip integration all together?
Think about these questions a bit.

 

[tcg]

Yup, good shout. I just managed it using the difference between initial and final potential energy as an expression for 1/2mv^2, then rearranged for v. thanks.

 

[HallsofIvy]

I am moving this to the Physics section.