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What is the value of the rotational of a rotational of a vector? Explain your calculus
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- Given the disk and density in Problem 11, derive an expression for the rotational inertia of this disk around an axis at theedge of the disk and perpendicular to the disks surface.Suppose the particles in the preceding problem have masses m1=0.10kg , m2=0.20kg , m3=0.30kg , m4=0.40kg . The velocities of the particles are . (a) Calculate the angular momentum of each particle about the origin. (b) What is the total angular momentum of the tour-particle system about the origin?(a) Calculate the rotational kinetic energy of Earth on its axis. (b) What is the rotational kinetic energy of Earth in its orbit around the Sun?
- Review. A small object with mass 4.00 kg moves counterclockwise with constant angular speed 1.50 rad/s in a circle of radius 3.00 m centered at the origin. It starts at the point with position vector 3.00im. It then undergoes an angular displacement of 9.00 rad. (a) What is its new position vector? Use unit-vector notation for all vector answers. (b) In what quadrant is the particle located, and what angle does its position vector make with the positive x axis? (c) What is its velocity? (d) In what direction is it moving? (e) What is its acceleration? (f) Make a sketch of its position, velocity, and acceleration vectors. (g) What total force is exerted on the object?A system of point particles is rotating about a fixed axis at 4 rev/s. The particles are fixed with respect to each other. The masses and distances to the axis of the point particles are m1=0.1kg , r1=0.2m , m2=0.05kg , r2=0.4m , m3=0.5kg , r3=0.01m . (a) What is the moment of inertia of the system? (b) What is the rotational kinetic energy of the system?Torque is a vector. Explain how you find both the magnitude as well as the direction of the torque vector in a given situation.
- An object travels along a path as shown below. A center of rotation is identified for the path. Answer the following question regarding the unit directions for the object traveling along the path. OA OB OD X Of the four vectors shown, which vector represents the un direction? OC Center of Rotation BDerive the equation for rotational work.Open Response 2: This is a multi-part problem. Please answer all parts here. A bat can be modeled as a long uniform rod rotated about one end. Treating a ball as a point particle and assuming it hits the end of the bat, such that the ball's momentum is perpendicular to the surface of the bat (as shown). Given the mass of the bat = 1.4 kg, the length of the bat = 0.75 m, the initial rotational velocity of the bat equal to 40-rad/s and the mass of the ball = 0.145 kg and the initial velocity of the ball equal to 20 m/s. a. What is the initial angular momentum of the bat/ball system? b. Assume that after being hit., the ball's velocity is equal and opposite to its initial velocity What is the bat's final angular velocity?
- A wheel (bottom wheel in the picture), with rotational inertia I, mounted on a vertical shaft with negligible rotational inertia, is rotating with angular speed wi. A nonrotating wheel ( top wheel in the picture) with rotational inertia 21 is suddenly dropped onto the same shaft as shown. a) Find the resultant angular velocity of the two wheels system. b) What is the ratio of the initial rotational kinetic energy to the final rotational kinetic energy? Demonstrate the answer in a form of KE; : KEfCan you explain how the parallel axial theorem applies to a? The wheel is spinning around its own axis within the system around the center axis.Needs Complete typed solution with 100 % accuracy.
