This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 4

2011 F = Ma, 7
Tags: 2011 , Problem 7
An ice skater can rotate about a vertical axis with an angular velocity $\omega_\text{0}$ by holding her arms straight out. She can then pull in her arms close to her body so that her angular velocity changes to $2\omega_\text{0}$, without the application of any external torque. What is the ratio of her final rotational kinetic energy to her initial rotational kinetic energy? (A)$\sqrt{2}$ (B) $2$ (C) $2\sqrt{2}$ (D) $4$ (E) $8$

2008 F = Ma, 7
Tags: 2008 , Problem 7
A toboggan sled is traveling at $\text{2.0 m/s}$ across the snow. The sled and its riders have a combined mass of $\text{120 kg}$. Another child ($m_{\text{child}} = \text{40 kg}$) headed in the opposite direction jumps on the sled from the front. She has a speed of $\text{5.0 m/s}$ immediately before she lands on the sled. What is the new speed of the sled? Neglect any effects of friction. (a) $\text{0.25 m/s}$ (b) $\text{0.33 m/s}$ (c) $\text{2.75 m/s}$ (d) $\text{3.04 m/s}$ (e) $\text{3.67 m/s}$

2010 F = Ma, 7
Tags: 2010 , Problem 7
Harry Potter is sitting $2.0$ meters from the center of a merry-go-round when Draco Malfoy casts a spell that glues Harry in place and then makes the merry-go-round start spinning on its axis. Harry has a mass of $\text{50.0 kg}$ and can withstand $\text{5.0} \ g\text{'s}$ of acceleration before passing out. What is the magnitude of Harry's angular momentum when he passes out? (A) $\text{200 kg} \cdot \text{m}^2\text{/s}$ (A) $\text{330 kg} \cdot \text{m}^2\text{/s}$ (A) $\text{660 kg} \cdot \text{m}^2\text{/s}$ (A) $\text{1000 kg} \cdot \text{m}^2\text{/s}$ (A) $\text{2200 kg} \cdot \text{m}^2\text{/s}$

2009 F = Ma, 7
Tags: 2009 , Problem 7
A bird is flying in a straight line initially at $\text{10 m/s}$. It uniformly increases its speed to $\text{15 m/s}$ while covering a distance of $\text{25 m}$. What is the magnitude of the acceleration of the bird? (A) $\text{5.0 m/s}^2$ (B) $\text{2.5 m/s}^2$ (C) $\text{2.0 m/s}^2$ (D) $\text{0.5 m/s}^2$ (E) $\text{0.2 m/s}^2$