Pictured on the right is a bar which has a length of L = 3.48 m. This diagram is from above looking down on the situation. The bar is free to rotate about a frictionless bearing represented by the dot in the center of the bar. Two forces are applied to the two ends as shown.F₁ = 1.86 N and F₂ = 3.18 N. This causes an angular acceleration of a 0.642 rad/2 (CCW). = What is the moment of inertia for the bar? Select one: a. b. OC. 5.04 kg m² 27.3 kg m² 2 13.7 kg m² d. 8.62 kg m² F1 Z|7| L L F₂

Use the worked example above to help you solve this problem. A merry-go-round modeled as a disk of mass M = 8.50 x 10¹ kg and radius R = 2.30 m is rotating in a horizontal plane about a frictionless vertical axle (see figure). (a) After a student with mass m = 80.0 kg jumps onto the merry-go-round, the system's angular speed decreases to 2.10 rad/s. If the student walks slowly from the edge toward the center, find the angular speed of the system when she reaches a point 0.490 m from the center. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. rad/s (b) Find the change in the system's rotational kinetic energy caused by her movement to the center. X Your response differs from the correct answer by more than 10%. Double check your calculations. J (c) Find the work done on the student as she or= 0.490 m.

A solid, uniform, spherical boulder (I=(2/5) MR2) starts from rest and rolls down a 75.0 [m] hill, as shown at the figure at the right. The top half of the hill is rough enough to cause the boulder to roll without slipping, but thelower half is covered with ice and there is no friction. What is the translational speed of the boulder when it reaches the bottom of the hill?

Please show formula's used and do step for step, please don't cut out any algebra

For question 4 answer A and B  4. A grinding wheel is spinning at a rate of 20.0 revolutions per second. When the power to the grinder is turned off, the grinding wheel slows with constant angular acceleration and takes 80.0 s to come to a rest. (a) What was the angular acceleration of the grinding wheel as it came to rest?   (b) How many rotations did the wheel make during the time it was coming to rest?

MII-1 Consider a solid disk of mass M and radius R, which has a uniform density. a) The disk is rotated about an axis that goes through its center and is perpendicular to its face, as shown in the diagram below on the left. Find a formula for its moment of inertia. Your answer should be a symbolic expression that only depends on the variables M and R. Hint: you will need to divide the disk into infinitesimal mass elements (dm) and then perform the integral: r?dm b) Suppose the radius of the disk is 12.5 cm and the mass is 1.75 kg. Use the formula from part a) to calculate a numerical value for the moment of inertia, in kg m2. c) Now the axis of rotation is moved from the center of the disk to the end of the disk, as shown in the diagram below on the right. Find an expression for its moment of inertia. Hint: theorem. As before, your answer should only depend on the variables M and R. d) Suppose the radius of the disk is 12.5 cm and the mass is 1.75 kg. Use the formula from part c) to…

Just explain concepts, formulas, theories as if you were to solve....   A hoop and a solid disk both have the same radius and mass and negligible thickness. Assume that they are both rotating with the same constant angular speed. Which has the higher rotational kinetic energy?   If you see an object rotating, is there necessarily a net nonzero torque acting on it? Why or why not?   A skater rotates quickly on the ice. He pushes his arms out. What happens to his angular speed? Why?   A 100 gram meter stick has a wad of clay on one end of it. The stick is supported from a fulcrum point 33 1/3 cm from the clay. What is the clay's mass?   A student sits on a rotating stool holding two 3.0 kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg m2 and is assumed to be constant. The student then pulls in the objects horizontally to 0.30 m…

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The 4.0 m long bar shown in the figure is fixed so that it can rotate freely around point O at the end of the bar. Three forces are applied along the bar at the positions and angles shown. Use the convention that a counter-clockwise spin is positive. Which of the following forces creates zero torque on the bar? Mark all that apply. 27 N 16 N 30 +3.0 m→ 45° - 4.0 m- 33 N The 33 N force The 16 N force The 27 N force None

A disk is rotating on a horizontal axis as shown in the figure. Answer the following questions if you pull out at A and push in at B along the axis of the disk.What is the direction of the torque acting on the disk? What is the direction of the initial angular momentum vector for the disk? The applied torque causes the wheel's axis (or angular momentum vector) to move. From the front view, what is the direction of motion of the L vector?     A disk is rotating on a vertical axis as shown in the figure. Answer the following questions if you push in at A and pull out at B along the axis of the disk. What is the direction of the torque acting on the disk? What is the direction of the initial angular momentum vector for the disk? The applied torque causes the wheel's axis (or angular momentum vector) to move. From the front view, what is the direction of motion of the L vector?