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2021 AP exam administration sample student responses AP physics c: mechanics free response question 3: set 1

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2021 AP Exam Administration Sample Student Responses AP Physics C Mechanics Free Response Question 3 Set 1 2021 AP ® Physics C Mechanics Sample Student Responses and Scoring Commentary Set 1 © 2021 Co[.]

2021 AP Physics C: Mechanics ® Sample Student Responses and Scoring Commentary Set Inside: Free Response Question R Scoring Guideline R Student Samples R Scoring Commentary © 2021 College Board College Board, Advanced Placement, AP, AP Central, and the acorn logo are registered trademarks of College Board Visit College Board on the web: collegeboard.org AP Central is the official online home for the AP Program: apcentral.collegeboard.org AP® Physics C: Mechanics 2021 Scoring Guidelines Question 3: Free-Response Question (a) 15 points point For using integral calculus to calculate the rotational inertia of the rod I = ∫r dm dm λ= dr γ x dx = point For correctly substituting γ x into the above equation = I dx ) ∫ x (γ x= 2 x=L x=L  x5    3M   L = γ = x dx γ = − 0      ∫ 5  L    x =0  x =0 ML2 Total for part (a) (b) point For using integral calculus to determine the center of mass of the rod = X CM points ∑i mi xi ∫ xdm = ∑i mi ∫ dm For correctly substituting γ x into the numerator of the above equation point For correctly substituting M into the denominator of the above equation OR evaluating the integral ∫ dm to find the mass of the rod point x=L x=L  γ x4   3M  L x dx γ   ∫   xλdx ∫ x γ x dx  x ∫=  = X CM L = = x 0= = =  L= M M M M M ( ) OR x=L x=L  γ x4  γ L4 γ x dx   ∫ x γ x dx  x ∫ xλdx = ∫= x 0= X= L = = = = CM = 2 x L= x L γ γ L L λ dx   γ x ∫ ∫x = γ x dx   3 x =0 ( ) Total for part (b) points © 2021 College Board AP® Physics C: Mechanics 2021 Scoring Guidelines (c) For selecting “Greater than” with an attempted justification point For a correct justification point Example responses for part (c) Because more of the mass of the rod is at the end of the rod opposite point P, more mass is concentrated away from the axis of rotation; thus, the rotational inertia of the rod would be greater around point P than around its center of mass OR According to the parallel axis theorem, I=Icm + md2, if the axis is at a position away from the center of mass, the rotational inertia is larger than if the axis were at the center of mass Total for part (c) points (d) For a concave down curve that decreases to zero for the graph of τ as a function of t point For a concave down curve that approaches horizontal for the graph of ω as a function of t point For consistency between the two graphs point Total for part (d) points (e) For selecting “Decreases” with an attempted justification point For a correct justification point Example responses for part (e) As the rod rotates downward, the angle θ in the torque equation τ=rFsinθ decreases Thus, the torque on the rod decreases OR As the rod rotates downward, the lever arm between point P and the rod’s center of mass continues to decrease; thus, the torque on the rod decreases Total for part (e) points â 2021 College Board APđ Physics C: Mechanics 2021 Scoring Guidelines (f) point For using conservation of energy to calculate the speed of the rotating rod U i + Ki = U f + K f Ui + = + K f Ui = K f point For correctly substituting into the above equation mghi = Iω f point For correctly solving for the linear speed of point S Mg ( ) ( 3 L = ML2 )( ) 3 MgL = Mv ∴ = v 10 v L = gL ( 9.8 m s2 ) (1.0 m=) 4.9 m s Total for part (f) points Total for question 15 points © 2021 College Board M Q3 A of M Q3 A of M Q3 A of M Q3 B of M Q3 B of M Q3 B of M Q3 C of        33           # '|l^F4OBoI4^| ^V|R?|J=OBlE|  4O

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