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# Momentum and Impulse

## Understand momentum as mass multiplied by velocity and impulse as change in momentum

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Spinning on Ice

### Spinning on Ice

Credit: Pietro Zanarini
Source: http://www.flickr.com/photos/7363465@N08/3725912776

Performed by every professional figure skater, the objective of the spin is to hold a specific body position while rotating around a single point on the ice.

#### News You Can Use

Credit: deerstop
Source: http://commons.wikimedia.org/wiki/File:Cup_of_Russia_2010_-_Yuzuru_Hanyu_(spin).jpg

Yuzuru Hanyu performing a sit spin [Figure2]

• A spin is accomplished by the skater rotating on the part of the blade that is just behind the toe pick. The various types of spins that are done depend on the position of the arms, legs and body of the skater. Even though there are various different spins, they all fall into one of three categories: upright spins, sit spins and camel spins. During some of the spins, it is common to see the rotation speed of the skater increase as an outstretched limb brought in closer. This is a result of the conservation of angular momentum.
• Angular momentum is the thing as ordinary translational momentum p\begin{align*}p\end{align*}, except it deals with velocities that are defined in rotational terms. Angular momentum is defined as

L=r×p=rmvsinθ\begin{align*}\overrightarrow{L} = \overrightarrow{r} \times \overrightarrow{p} = rmv \sin \theta\end{align*}

And just like the previous discussion of translational momentum, angular momentum must be conserved.

ΔLLfinal=LfinalLinitial=0=Linitial\begin{align*}\Delta L&= L_{final} - L_{initial}=0 \\ \rightarrow L_{final} &= L_{initial}\end{align*}

So when an ice skater who is spinning with a given angular velocity ω\begin{align*}\omega\end{align*}, brings an outstretched limb closer, r\begin{align*}r\end{align*} becomes smaller. Since angular momentum must be conserved, the angular velocity ω\begin{align*}\omega\end{align*} must increases since r\begin{align*}r\end{align*} decreases.

#### Show What You Know

Using the information provided above, answer the following questions.

1. When the water bottles were brought closer to Bill's body in the video, why did he speed up?
2. Is the angular velocity and the angular momentum parallel or perpendicular to one another?

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