A physical system is invariant under rotation about a fixed axis. Then the following quantity conserved: Total Angular Momentum. Linear momentum along the axis of rotation. Angular Momentum along the axis of the rotation. Total Linear Momentum.
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- A point particle travels in a straight line at constant speed, and the closest distance it comes to the origin of coordinates is a distance l. With respect to this origin, does the particle have nonzero angular momentum? As the particle moves along its straight-line path, does its angular momentum with respect to the origin change?3)A bug of mass m_bug = 0.20 kg is sitting on your favorite record when youdecide to turn on the record player. Your record is a solid disk of radius R = 15cm and mass m disk = 0.70 kg. Your system revs up to a constant angularspeed 2 revolutions per second. The bug is initially sitting at a distance R/2 = 7.5cm, but being a thrill seeker decides to walk to the very edge of the record atradius R. What is the final Moment of Inertia for the system when the bugchanges its position? Assuming that angular momentum is conserved, what isthe final angular speed of the system when the bug has reached the edge? Whatis the bug's linear speed now?A star originates as a large body of slowly rotating gas.Because of gravitational attraction, this large body of gas slowly decreases in size.You can assume that no external forces are acting.Which one of the following statements correctly describes what happens as the radius of the body of gas decreases? Both the moment of inertia and the angular velocity increase. Both the angular momentum and the angular velocity increase. The angular momentum increases and the angular velocity decreases. Both the angular momentum and the angular velocity decrease. The angular momentum remains constant and the angular velocity increases.
- 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.12–158. An airplane is flying in a straight line with a velocity of 200 mi/h and an acceleration of 3 mi/h². If the propeller has a diameter of 6 ft and is rotating at a constant angular rate of 120 rad/s, determine the magnitudes of velocity and acceleration of a particle located on the tip of the propeller.A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 10 rev/s; 60 revolutions later, its angular speed is 15 rev/s. Calculate (a) the angular acceleration (b) the time required to complete the 60 revolutions (c) the time required to reach the 10 rev/s angular speed (d) the number of revolutions from rest until the time the disk reaches the 10 rev/s angular speed
- 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?). [216-146. A ride in an amusement park consists of a rotating arm AB that has an angular acceleration of aдB = 1 rad/s² QAB when @AB = 2 rad/s at the instant shown. Also at this instant the car mounted at the end of the arm has an angular acceleration of a = {-0.6k) rad/s² and angular velocity of w' (-0.5k) rad/s, measured relative to the arm. Determine the velocity and acceleration of the passenger C at this instant. = w' = 0.5 rad/s 10 ft 60° y WAB = 2 rad/s 30° x Probs. 16-145/146 B 2 ft
- Thank you. Shouldn't rotational kinetic energy be used, though, for part (b)?Conservation of Angular Momentum Given data on two disks, such as masses and inner/outer diameters/radii, and the initial angular velocities of the 2 disks, use the conservation of angular momentum principle to calculate the common angular velocity after the two disks are allowed to contact each other and spin together. Or, given the common final angular velocity, solve for unknowns such as the initial angular velocity of one of the disks. Or, given data on the starting and final angular velocities and some data on the disks, solve for unknowns such as moments of inertia, masses or diameters/radii. EXAMPLE Two metal disks have masses m1=3.45 kg and m2=UNKNOWN kg, and each has a radius of 8.31 cm. (You may ignore the inner hole for both disks assume that it is very small.) They spin on cushions of air in a standard rotational dynamics apparatus. Initially, disk #1 is spinning counterclockwise at 6.02 rad/s and disk #2 is spinning clockwise at 2.50 rad/s. A pin is removed that drops disk…Number 12