Paul Hewitt's "Figuring Physics" in the Feb. 2016 issue asked whether it would take a larger velocity change to stop a satellite in a circular orbit or to cause it to escape. An extension of this problem asks: What "minimum" velocity change is required to crash a satellite into the planet, and how does that compare with the…

In the teaching and learning of physics, simulations have many applications. Simulations can help to illuminate concepts (such as the motion of electrons in electric or magnetic fields) that cannot usually be seen with the unaided eye, or to slow down things that happen over short time periods or at high speeds. They can also be used to help…

Races between moving objects are an engaging way to teach dynamics to introductory physics students. One standard example consists in racing hollow and solid cylinders as they roll down an inclined plane. Another striking demonstration is a race between two marbles on side-by-side tracks that start and end together, but with one track taking a…

An ice hockey player can strike a puck at speeds up to about 45 m/s (100 mph) using a technique known as the slap shot. There is nothing unusual about the speed, since golf balls, tennis balls, and baseballs can also be projected at that speed or even higher. The unusual part is that the player strikes the ice before striking the puck, causing the…

In popular accounts of the time dilation effect in Einstein's special relativity, one often encounters the statement that moving clocks run slow. For instance, in the acclaimed PBS program "NOVA," Professor Brian Greene says, "[I]f I walk toward that guy... he'll perceive my watch ticking slower." Also in his earlier piece for The New York Times,…

A rattleback is a well-known physics toy that has a preferred direction of rotation. If it is spun about a vertical axis in the "wrong" direction, it will slow down, start rocking from end to end, and then spin in the opposite (i.e. preferred) direction. Many articles have been written about rattlebacks. Some are highly mathematical and…

How far, in space, can we see? And can we see an object whose Hubble recessional velocity exceeds the speed of light? Maybe you've thought about these questions before, or perhaps you've seen them discussed in the literature or mentioned in the media. With the recent popularity of inflation and Big Bang cosmology, they're hard to avoid. The…