Rotation Quiz True or False

1. What is the minimum speed a roller coaster can be traveling and still successfully navigate a 20 m tall circular loop? -> 9.9 m/s
2. It takes a pitching machine's main drum sixteen full revolutions to reach its max speed of 1000 rad/s. What is the drum's angular acceleration? -> 9947 rad/s2
3. What is the moment of inertia of a tetherball? The ball has an 8 cm radius and weighs 1.5 kg, and spins around a pole on a 1.5 m rope (attached to the center of the pole and the top of the tetherball). -> 3.38 kg · m2
4. The moment of inertia of a cube about any axis through the center of one of its faces is , where s is the length of the cube's sides. What is the change in angular momentum of a six-sided die (side length 1.8 cm, weight 9 g) when it's tumbled out of a Dungeon Master's hand, increasing its rotational speed from 10 rad/s to 30 rad/s? -> 97.2 g · cm2/s
5. The plank in a pirate ship is 3 m long and weighs 100 kg. It is balanced on the edge of the ship's deck, with 1 m of plank extending off the ship over the ocean. How far out off the edge of the ship can a 40 kg prisoner walk before the plank starts to tip? -> 0.4 m
6. When a record starts to spin, the turntable applies a constant torque to the record in order to accelerate it. After 1 s, the record has made two full rotations. If the torque continues to be applied, how many rotations will the record have made by the end of 3 s? -> 6
7. A bike tire is spun with a torque of 60 N · m due to the rider pushing on the pedals. The 70 cm diameter tire has a coefficient of rolling friction with the asphalt of 0.01, and carries half the weight of the bicycle and rider (the other half is carried by the bicycle's other tire): 80 kg. What is the resulting net torque on the tire? -> 57.3 N · m
8. -> 50.6 kJ
9. A car's engine can exert 150 N · m of torque on one of its wheels, 40 cm in diameter. What power is required to move the wheel along the road at 90 km/hr? -> 18.7 kW
10. A ball, a cylinder, and a tube of equal mass and radius are placed on top of a (frictionless) hill. Which reaches the bottom first? -> The ball

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