ON THE ATTACHED I UPLOAD THE PROBLEM FOR THE figure (9) A disk ( Icm = 12 MR2 )

Question

ON THE ATTACHED I UPLOAD THE PROBLEM FOR THE figure

(9)  A disk ( Icm = 12 MR2 ) of mass 2.00 kg and radius 0.200 m is spinning clockwise at 10.0 rad/s and it

is sliding across a frictionless horizontal surface at 21.0 m/s. It runs into an initially stationary ring( Icm = MR2 ) of mass 1.00 kg and the same radius, 0.200 m, and the two stick together and move off, spinning, after the collision. Before the collision, the spinning disk’s center of mass was moving along a
line tangent to the edge of the ring

Find (a) the velocity of the center of mass of the spinning disk + ring system after the collision, (b) the angular velocity of the spinning system after the collision, and (c) the % kinetic energy lost as a result of the collision.

Suggestion: The center of mass moves at constant velocity throughout this collision, and the total angular momentum of the system about its center of mass is constant throughout. You will need to apply the parallel axis theorem to find the total moment of inertia of the hoop + ring about the center of mass.

6) (a) Use integration to calculate the rotational inertia of a uniform solid thin rod of length L and mass M, about an axis perpendicular to the rod and passing through the rod ¼ of the way from its center. (b) Check your answer by using the moment of inertia of the rod about an axis perpendicular to the center of the rod and passing through its center of mass ( 1 12 ML2 ) and applying the parallel-axis theorem. Suggestions: Pattern your calculation after Example 9.10 in your text. The integration, 2 rdm , can be carried out by using elements of mass obtained by dividing into infinitesimal length elements, dx, along the rod (setting x=0 at the rotation axis) and then using the mass per unit length of the rod, / ML, to construct the element of mass, dm = M / L ( )dx

(10)  Pulled Rolling Disk  A constant horizontal force of 9.0 N is
applied to a uniform solid cylinder by fishing line that is wrapped around it. The mass of the cylinder is 10.0 kg and its radius is 0.10 m. There is static friction sufficient to ensure that the cylinder rolls without slipping on the horizontal surface.

(a) What is the acceleration of the center of mass of the cylinder?(b) What is the magnitude of the angular acceleration of the cylinderabout its center of mass?(c) What is the friction force (both magnitude and direction) that acts on the cylinder?

Explanation / Answer

As per guide lines i did first problem

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