Write down the Gradient, Divergence and Rotational Theorems.
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Write down the Gradient, Divergence and Rotational Theorems.
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- Solution for this problem, please. It involves the use of torque and angular acceleration.Start with a freely rotating hoop-like wheel of mass m = 30kg and radius 25cm, rotating at 125 rpm.1. Sketch this wheel, write out equations for and calculate it’s L and rotational KE.The wheel hits the ground, bounces and skids while negative accelerating, eventually locking to the ground so that its linear velocity equals its rotational velocity times its radius.2. Write this (roll no slip) equation. Sketch this final rolling wheel on the ground, include a vector for the linear velocity.3. Write an equation conserving angular momentum before and after the drop. Solve your equation for final angular velocity (both algebra and a number). Briefly explain.4. Solve for final rotational and linear kinetic energy and compare to initial rotational energy. How much energy was lost during the skidding process? (Formula and number).Please show formula's used and do step for step, please don't cut out any algebra
- A vertical rectangular object of uniform mass M = 7 kg has sides a = 0, 26 m and b = 0,58 m. It is pivoted from point O as shown in the figure below. If a constant force of F = 109 N along the diagonal is applied as shown below, determine the angular acceleration of the rectangle in SI units at the instant shown. Express your answer using one decimal place. Please use the convention: Clockwise (+), Counterclockwise (-) when expressing your answer. Hint 1: The moment of inertia of a uniform disk about an axis of rotation passing through the center of mass (CM) is ICM = 1½M(a²+b²). Hint 2: Don't forget the force of gravity!!! Take g = 9.80 m/s². a CM 0 b FBelow is a sketch of the toy on a rotor ride at the moment after the floor drops. The rotor has a radius of R and the toy has mass m. Assume the angular velocity is constant, and the toy is not slipping downward. write Newton’s Second Law for the x and y directions. Use algebra and your equations above to predict the minimum angular velocity ωmin necessary to keep the toy “stuck” to the side of the rotation tube. Express your answer in terms of g, μs, R. (nonumbers yet). Show all of your work and your final result below.Be sure to review Examples 10.11 and 10.12 (Section 10.6) before attempting these problems. Suppose that instead of hitting the center of the door, the bullet in (Figure 5) strikes the door at the edge farthest away from the hinge and embeds itself there. What is the angular speed of the door just after the bullet embeds itself? Take Vbullet = 320 m/s. Express your answer in radians per second. 1να ΑΣφ. W = rad/s Submit Request Answer Figure 5 of 5 > Part F Hinge What fraction of the initial kinetic energy of the bullet remains as kinetic energy after the collision? l= 0.50m Express your answer using two significant figures. m = 10g Bullet να ΑΣ φ. Voullet d = 1.00m M =15kg K2/K1 = Submit Request Answer Before After