SAT Physics Help

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1

<p>Ok so I think I'm still confused by the concept of angular momentum and when to use it in a problem.</p>

<p>I was doing the Sparknotes practice test, and I came upon this problem:</p>

<pre><code>Questions 44–45 refer to a planet of mass m orbiting a star of mass M at speed v. The orbit is circular with radius R.
</code></pre>

<ol>
<li> What would the planet’s velocity be if it orbited at a radius of 2R?</li>
</ol>

<p>The answers were:</p>

<p>(A) v/2
(B) v/sqrt(2)
(C) v
(D) sqrt(2)v
(E) 2v</p>

<p>I chose B and got the right answer by using the equation mv^2/R=GMm/R^2 and then solving for v. I also understand this conceptually because I know that the gravitation force between the two planets is the source of the centripetal force. However, why can't I use angular momentum to solve this problem? Namely, the equation L=mvr. According to the angular momentum equation, if radius is doubled, then velocity should be halved. Also, in what situations/type of problem should I be using angular momentum?</p>

2

<p>

Because there is nothing in this problem that says the angular momentum is conserved. There is no mention of only force being passing the center that gives zero torque… </p>

<p>For example, if the problem states -
the force applies to the system passes the center of the mass (like a person spinning), then the torque is zero. Therefore, L doesn’t change. But in this one, apparently, L changes. Without L change, (external force/torque) the planet couldn’t change orbit.</p>

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<p>…why is the answer b?</p>

4

<p>The centripetal force provides the gravitational force so ((mv^2)/R)=((GmM)/R^2) and solving for v yields v=sqrt((GM)/R). Because the radius is doubled, you have sqrt((GM)/(2R)) = (1/sqrt(2))(sqrt(GM)/R) and because v=sqrt((GM)/R), the answer, by substitution, is v/sqrt(2) = B</p>

5

<p>thanks! 10 char</p>