49. Three objects lie in the x, y plane. Each rotates about the z axis with an angular speed of 6.00 rad/s. The mass m of each ob- ject and its perpendicular distance r from the z axis are as follows: (1) m, = 6.00 kg and r, = 2.00 m, (2) m, = 4.00 kg and r, = 1.50 m, (3) m; = 3.00 kg and r3 = 3.00 m. (a) Find the tangential speed of each object. (b) Determine the total kinetic energy of this system using the expression KE = }m,v² + ¿mv? + ±mv3. (c) Obtain the moment of inertia of the system. (d) Find the rotational kinetic energy of the system using the relation KEg = }lw² to verify that the answer is the same as the answer to (b).

49. Three objects lie in the x, y plane. Each rotates about the z axis with an angular speed of 6.00 rad/s. The mass m of each ob- ject and its perpendicular distance r from the z axis are as follows: (1) m, = 6.00 kg and r, = 2.00 m, (2) m, = 4.00 kg and r, = 1.50 m, (3) m; = 3.00 kg and r3 = 3.00 m. (a) Find the tangential speed of each object. (b) Determine the total kinetic energy of this system using the expression KE = }m,v² + ¿mv? + ±mv3. (c) Obtain the moment of inertia of the system. (d) Find the rotational kinetic energy of the system using the relation KEg = }lw² to verify that the answer is the same as the answer to (b).

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Q1
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1. A 50-kg girl rides on a giant Ferris wheel of radius 12 m that makes 2 revolutions each minute. (a) (b) What is the girl's speed in m/s? What is the apparent weight of the girl at the lowest point in the ride? (Hint: Her apparent weight is equal to the force of the seat acting on her). ) What is the apparent weight of the girl at the highest point in the ride? If she felt weightless at the top of the ride, how fast would she be moving? (c) (d) Show transcribed image text 1. A 50-kg girl rides on a giant Ferris wheel of radius 12 m that makes 2 revolutions each minute. (a) What is the girl?s speed in m/s? (b) apparent weight is equal to the force of the seat acting on her). (c) in the ride? (d) I What is the apparent weight of the girl at the lowest point in the ride? (Hint: Her What is the apparent weight of the girl at the highest point If she felt weightless at the top of the ride, how fast would she be moving?
4. A pottery wheel of radius 20cm and mass M is freely rotating about an axis through its center at 87 rads/s. A blob of very dense clay of mass 5kg is gently placed on the spinning wheel halfway up its radius (i.e. 10cm from the axis of rotation). This causes the rate of rotation of the pottery wheel to drop to 7.8a rads/s. You can treat the pottery wheel as a uniform disk and the blob of clay as a point particle. The moment of inertia of a disk about an axis through its center is given by I = MR. (a) Write down expressions for the angular momentum of the system before and after the blob has been placed on the wheel. (b) Hence, find the mass M of the pottery wheel.
2. A small nail stuck in your car tire moves on a circular path with a radius of 35 cm. When the nail has traveled a linear distance of 5.5 m, through what angle has the tire rotated? Give your answer in radians and degrees. (Answers: 0 = 16 rad, 0 = 900°)