A wheel has a radius of 2.19 m. How far (path length) does a point ...

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A wheel has a radius of 2.19 m. How far (path length) does a point on the circumference travel if the wheel is rotated through the following angles, respectively? (a) 34.5 rad (b) 34.5° (c) 34.5 rev 2) A dentist's drill starts from rest. After 4.89 S of constant angular acceleration it turns at a rate of 2.59 X 104 rev/min. (a) Find the drill's angular acceleration. (b) Determine the angle (in radians) through which the drill rotates during this period. 3) In 1931 a man named M. Goventosa built the monowheel shown below. This one wheeled motorcycle's wheel maximum angular velocity was about 436 rev/min. A) Given that it's radius was 0.920 m, what was the largest linear velocity of the monowheel? B) The monowheel could not accelerate fast or the rider would start spinning inside (this is called "gerbiling"). The maximum angular acceleration was 10.9 rad/s². How long, in seconds, would it take it to hit maximum speed from rest? 4) It has been suggested that rotating cylinders about 5.78 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth? 1 mile = 1609 m 5) In the movie Ant-man there is a scene where Ant-man is riding on a turntable. A record has an angular velocity of 33.3 rev/min. If Ant-man, while small, stands 14.9 cm from the center of the record, what minimum coefficient of friction is needed to keep Ant-man from flying off? 6) An air puck of mass m1 = 0.184 kg is tied to a string and allowed to revolve in a circle of radius R = 1.04 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of m2 = 0.94 kg is tied to it (see the figure below). The suspended mass remains in equilibrium while the puck on the tabletop revolves. m R 12 (a) What is the tension in the string? (b) What is the horizontal force acting on the puck? (c) What is the speed of the puck? 7) A roller-coaster vehicle has a mass of 421.8 kg when fully loaded with passengers (see figure). B 10 m 15 m A a) If the vehicle has a speed of 18.1 m/s at point 4, , what is the force of the track on the vehicle at this point? (b) What is the maximum speed the vehicle can have at point Rin order for gravity to hold it on the track? 8) In the comics, movies, and Norse mythology the god Thor flies by spinning his hammer, Mjölnir, really fast from a leather strap at the end of the handle, letting go, then grabbing it and having it pull him. This is completely nonsensical, but lets pretend he can do this. If Thor wants to reach escape velocity (velocity needed to leave Earth's atmosphere), he will need the linear velocity of the center of mass of the hammer to be 11,200 m/s. a) If the distance from the end of the strap to the center of mass of the hammer is 0.372 m, what angular velocity does Thor need to spin his hammer at to reach escape velocity? b) If the hammer starts from rest what angular acceleration does Thor need to reach that angular velocity in 4.60 s? c) While the hammer is spinning at its maximum speed what impossibly large tension does the leather strap, which the hammer is spinning by, exert when Mjölnir is at its lowest point? Mjölnir has a total mass of 20kg. 9) In the movie X-Men: Days of Future Past, the mutant Quicksilver runs around a circular room so fast that he can run on the walls, as shown below. A) If the room's radius is 17.9 m, at what minimum speed does Quicksilver need to run to stay on the walls without sliding down? Assume the coefficient of friction between Quicksilver and the wall is 0.238. From Above From Side wall 10) The pilot of an airplane executes a constant-speed loop-the-loop maneuver in a vertical circle as in the figure below. The speed of the airplane is 2.2X10² m/s, and the radius of the circle is 3.0 X 10³ m. R (a) What is the pilot's apparent weight at the lowest point of the circle if his true weight is 763 N? Hint: Apparent weight is the normal force between the pilot and the chair. Also, the true weight is a weight and not a mass. (b) What is his apparent weight at the highest point of the circle? (c) What speed would have resulted in the pilot experiencing weightlessness at the top of the loop?

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