## Illustration 9.3: The Zero-Momentum Frame

reference frame relative velocity: v = m/s

Is physics different when viewed in different reference frames? Well, it can certainly look different. Consider the collision in the animation as seen initially in the reference frame of Earth (the relative velocity between this frame and Earth's stationary frame is zero). Here both the red ball and the blue ball have the same mass equal to 1 kg. Note that energy and momentum are conserved in the collision with kinetic energy = 2 J and px = 2 kg·m/s before and after the collision. Restart.

Change the velocity from zero to 2 m/s (position is given in meters and time is given in seconds). How does the collision change? The red ball is now initially stationary and the blue ball is moving to the left at 2 m/s. Note that, in the original collision with v = 0 m/s, the red ball was initially moving to the right and the blue ball was initially stationary. In the new frame the momentum of the two-ball system is different. However, the kinetic energy happens to be the same and energy and momentum are conserved.

Now try v = -2 m/s. Are energy and momentum still conserved? Even though the values of the kinetic energy and momentum change, the laws of conservation of energy and conservation of momentum still hold.

Now try v = 1 m/s. What is the new momentum for the two-ball system? This frame of reference is appropriately called the zero-momentum frame. In this frame the momentum of the system is zero. This frame is also called the center-of-mass frame. The center of mass is a coordinate that is a mass-weighted average of the positions of the objects that make up the system. In a two-object system the center of mass is always somewhere in between the two objects. Since the center of mass is a mass-weighted average, the center of mass will always be closer to the object that is more massive. In the case of this animation, where both balls have the same mass, the center of mass is always at the midpoint between the two masses. This point does not move in the zero-momentum frame, but does move in other frames.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.

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