- #1

- 188

- 1

## Homework Statement

A stone falls from rest from the top of a building. Which of the following graphs' shapes best represents the stone's angular momentum L about the point P as a function of time?

http://img413.imageshack.us/img413/1033/54161793ev0.png [Broken]

a) L = 0

b) L = c (constant)

c) L = c * t (linear in t)

d) L = t^2

e) L = upside-down parabola with vertex at some positive x and positive y, passing through the origin

## The Attempt at a Solution

I think I solved this problem using the definition of angular momentum as the cross product of

**r**and

**p**(calling point P (x_0, y_0)):

[tex]\vec{L} = \vec{r} \times \vec{p} = \left| \begin{array}{ccc}

\hat{i} & \hat{j} & \hat{k} \\

r_x & r_y & 0 \\

0 & p_y & 0 \end{array} \right| = r_x p_y \hat{k} = x_0 m g t \hat{k}[/tex]

where [itex]r_x = x_0[/itex] and [itex]p_y = - m g t[/itex]

So apparently linear momentum is linear in time. This question is for an AP Physics C sample multiple choice, so I have a hard time believing they want us to evaluate a cross-product to figure out this. Is there some intuitive way to understand this? Or a quick way to do it? I tried using the definition of cross product as [itex]r p \sin(\theta)[/itex] but that doesn't get me very far either.

Last edited by a moderator: