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conservation of angular and linear momentum

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(1)
A particle of mass m at the end of a light string wraps itself about a fixed vertical cylinder of radius a. All the motion is in the horizontal plane. the angular velocity of the cord is w0 when the distance from the particle to the point of contact of the cylinder and string is b. find the angular velocity and tension in the string after the cord has turned an additional angle q.

(2)
A deuteron with speed of 14.9 km/s collides elastically with a neutron at rest. Use the approximation that the deuteron is twice the mass of the neutron.
If the deuteron is scattered in the LAB angle psi=10,

a. what are the final speeds of the deuteron and neutron?
b. What is the LAB scattering angle of the neutron?
c. What is the maximal possible scattering angle of the deuteron?

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The solution gives a step by step explanations regarding the two problems.

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