Question

Can you please solve part a, b , c. d and e with explaining the concepts and steps

2018 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS λ-(2 )- none uniforme densi y 3. A triangular rod, shown above, has length L, mass M, and a nonuniform linear mass density given by the equation λ 2Af ー『x . where is the distance from one end of the rod. (a) Using integral calculus, show that the rotational inertia of the rod about itsleft end is (MIET Figure Figure 2 a rotational inertia around its center of MI 2 The thin hoop shown above in Figure I has a mass M, radiusand a Three rods identical to the rod from part (a) are now fastened to the thin hoop, as shown in Figure 2 above. (b) Derive an ex or of the hoop-rods system about the center of tbe hoop. Express your answer in terms ond Poysical constants,as ppropriate. The hoop-rods system is initially at rest and held in place but is free to rotate around its center, A constant force is exerted tangent to the hoop for a time ) Der ve an expresso nfor the final angular speed ω of the ho SPIN- rods system. Express your answer in terms of M, L, F, Δ, and physical constants, as appropriate. O 2018 The Colege Board Visit the College Board on the Web: www.collegeboard.org GO ON TO THE NEXT PAGE

Answer 1