Ex. 65: Calculate the angular momentum of the earth due to rotation about its own axis. Assume that the earth is a sphere of mass 6 x 1024 kg and radius 6400 km. (Oct 1987)
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- 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).9. The earth has an angular speed of 7.272 × 10−5 rad/s in its rotation. Find the new angular speed if an asteroid of mass m = 102² kg hits (and sticks to) the earth while traveling at a speed of 1.40 × 10³ m/s (assume the asteroid is a point mass compared to the radius of the earth) in each of the following cases: (a) The asteroid hits the earth dead center. (b) The asteroid hits the earth nearly tangentially in the direction of the earth's rotation. (c) The asteroid hits the earth nearly tangentially in the direction opposite to the earth's rotation.Problem 5) (Conservation of angular momentum) Before A merry-go-round with a radius of 2.5 meters and mass of M = 175 kg has an angular velocity of 0.5 rev/s. A boy with a mass of m = 25 kg runs and jumps tangentially on the edge of the merry- go-round and holds on the rail. What is the final angular speed of the boy+merry-go-round? (Hint: the initial angular momentum of the kid is mass times velocity times the radius, i.e., mvr, and his final moment of inertia is mr?). [
- 2When the Sun runs out of nuclear fuel it will collapse into a white dwarf. The present radius of the Sun is R, and the mass is M,. The angular velocity of the Sun is wo. After the Sun collapses into a white dwarf, the radius is R/108. What is the rotational energy of the Sun after it collapses? Assume the Sun loses no mass. - MRw? 5(108“) MRw? 5(108) - MRw? 5(1082) O 1084 - MRw? 108 108° - M Rw? 5We will assume that the velocity of Juan's hand and the pencil were both 0.9 meters per second prior to impact and that his wrist added an angular velocity to the pencil of 7.4 radians/second. In reality the pencil dug in nearest to my thumb and did not poke through the back. For the purpose of this calculation we will instead say that the blue pencil of mass M and length of L pushed through my hand until 20% of its length was behind the hand. We will further assume that the normal force between the hand and the pencil was 120 Newtons and that the area of the point of the pencil was 0.0024mm2. The coefficient of kinetic friction between the pencil exterior and my flesh was 0.24 because I was running a slight fever and had a temperature of 102 degrees Fahrenheit. Write an expression for dm: dm = Write the result for the Moment of Inertia: I = The formula for Moment of Inertia in the form of an integral: I = ∫ Write an expression for the upper limit of the integral: Upper Limit…
- Assume mars is a uniform solid sphere of mass 6.42x10^23 kg and a radius 3390 km.The length of a day on mars is 24 hours and 37 min. What is the rotational kinetic energy of the planet about its axis.la) A “dumbbell" used in the energy conservation in rotational motion lab, consists of a cylindrical rigid rod with two 0.2 kg masses fixed at the ends. The mass of the rod is negligible when compared to the two masses. The diameter of the rod is 8 mm and its length is 20 cm. The rod is rotating about its center (with the axis of rotation perpendicular to the length of the rod as in today's experiment). What is the moment of inertia of this system?A compact disk (CD) in the computer rotates with a speed of 750 revolutions per minute A-express the angular speed of the CD IN THE unit of radian/ sec B- how long it takes for the CD to complete 7 revolutions