- The centre of mass of the disk undergoes simple harmonic motion with angular frequency o equal to k 9. 41/17 M (a) (b) 2k M (c) 2k √3M (d) 4k √3M
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- A circular disc of mass M and radius R is rotating about its axis with angular speed ω1 . If another stationary disc having radius R/2 and same mass M is droped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω2. The energy lost in the process is p% of the initial energy. Value of p isThe velocity of the 8-kg cylinder is 0.3 m∕s at a certaininstant. The mass of the grooved drum is 12 kg, its centroidal radiusof gyration is k = 210 mm, and the radius of its groove isri = 200 mm. The frictional moment at O is a constant3 N∙m. Find the frictional force if final speed is given to be 2.5.A uniform, thin, spherical shell of radius, R, and mass, m, is rolling without slipping or sliding on a level surface. If the center-of-mass velocity of the ball is vCM what is the total kinetic energy of the 2 MR? ball? Hint: cm,shell VCM IR Contact Point O a. 1my? ,2 ст 2 b. 7 mv2 10 ст С. ту2 ст d. 5 ,2 -mv ст 3 е. mv2 4
- 3 z, 0 = -1.5z. 13-99. A car of a roller coaster travels along a track which for a short distance is defined by a conical spiral, r = where r and z are in meters and 0 in radians. If the angular motion 0 = 1 rad/s is always maintained, determine the r, 0, z components of reaction exerted on the car by the track at the instant z=6 m. The car and passengers have a total mass of 200 kg. Prob. 13-99A playground merry-go-round with an axis at the center (radius R = 1.5 m and rotational inertia | = 1.33 x 103 kgm²) is initially rotating at angular velocity wo = 1.1 rad/s (counter-clockwise). A girl of mass m = 39 kg is running at speed vo = 3.3 m/s in a direction tangent to the disk of the merry-go-round, intending to jump on to the point labeled with the green "x" (she is indicated by the purple circle in the figure). What is the angular momentum of the girl relative to the rotation axis of the merry-go-round? Your answer should be in kgm²/s, but enter only the numerical part in the box. R WoA physical pendulum consists of a vertical board of of mass 5.8 kg, length 172 cm, and width 5 cm hanging from a horizontal, frictionless axle. A bullet of mass 145 g and a purely horizontal speed v impacts the pendulum at the bottom edge of the board. The board then makes a complete circle. (a) If the bullet embedded itself in the board, what is the minimum speed the bullet could have to make this so? (b) If the bullet passed through the board, reducing its speed by 1/5 its original value, what is the minimum speed of the bullet? (c) If the bullet is made of rubber and rebounds elastically, what is the minimum speed the bullet could have? (d) What is the rebound speed of the bullet?
- 11.41. A 2.0-kg block starts from rest on the positive x axis 3.0 m from the origin and thereafter has an acceleration given by a = 4.0i - 3.0j in m/s2. The torque, relative to the origin, acting on it at the end of 2.0 s is: O O O O 0 N·m (-18 N.m)k (+24 N-m)k (-144 N-m)k (+144 vA uniform solid disk of mass m = 2.99 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 6.05 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. kg • m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim? kg • m2/sA 9.93 kg particle with velocity ?→=(9.25m/s)?̂ −(6.52m/s)?̂v→=(9.25m/s)î-(6.52m/s)ĵ is at x = 9.15 m, y = 6.63 m. It is pulled by a 9.15 N force in the negative x direction. About the origin, what are (a) the particle's angular momentum, (b) the torque acting on the particle, and (c) the rate at which the angular momentum is changing?
- A uniform solid disk of mass m = 2.99 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 5.99 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. |kg · m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim? |kg · m2/sTwo identical tops, #1 and #2, spin with angular velocities ω1 = 10 rad/s counterclockwise and ω2 = 12 rad/s clockwise. The tops bump into one another and separate. After the collision, the first top has angular velocity of 5 rad/s counterclockwise. During the collision, the force of impact is along the line connecting the centers of the top, so no torque is exerted on either top. What is the magnitude of the angular velocity of the second top? Does the top spin clockwise or counterclockwise?A playground merry-go-round has a radius of R = 4.0 m and has a moment of inertia Icm = 7.0 x 10³ kgm² about an axis passing through the center of mass. There is negligible friction about its vertical axis. Two children each of mass m = 25 kg are standing on opposite sides a distance ro = 3.0 m from the central axis. The merry-go-round is initially at rest. A person on the ground applies a constant tangential force of F= 2.5 x10² N at the rim of the merry-go-round for a time At =1.0 x 10¹ s. اناما R a. What is the magnitude of angular acceleration of the merry-go-round? b. What is the angular speed of the merry-go-round when the person stopped applying the force? c. What is the rotational kinetic energy of the merry-go-round when the person stopped applying the force? d. The two children then walk inward and stop a distance of r1 =1.0 m from the central axis of the merry-go-round. What is the angular velocity of the merry-go- round when the children reach their final position? What is…