Centripetal acceleration test answers and mark scheme for AP Physics 1 (free PDF download)

The questions are on the centripetal acceleration test. Take it under real conditions before reading the mark scheme.

Quick answer: Uniform circular motion is travel at constant speed along a circle. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics 1 test on centripetal acceleration, from arrows at one point to linear graph, with the equivalent answers to accept.

Centripetal acceleration test answers and mark scheme for AP Physics 1 (free PDF download)

Model answers with a marking guide. Award the mark for a correct method even when an arithmetic slip follows, and apply the unit and significant-figure conventions used in the course.

Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 2

Contents

Question 1 Arrows at one point (2 marks)

A (tangent to the path, in the direction of motion).
B (toward the centre).

Marking: 1 mark for each correct arrow.

Question 2 Control-line aircraft (3 marks)

v = 2π r / T = 2π(8.0) ÷ 2.5 = 20 m/s.
a_c = v² / r = 404 ÷ 8.0 = 51 m/s².
T = m a_c = 0.50 × 50.5 = 25 N.

Marking: 1 mark per part; allow 25 N from 20.1 m/s.

Question 3 A heavier, bigger planet (2 marks)

g ∝ M / R², so the ratio is 4 ÷ 2² = 1.
W = 60 × 9.81 = 5.9 × 10² N, the same as on Earth.

Marking: 1 mark for each correct answer.

Question 4 Titan around Saturn (3 marks)

v = √(G M / r) = √(6.67 × 10⁻¹¹ × 5.68 × 10²⁶ ÷ 1.22 × 10⁹) = 5.57 × 10³ m/s.
T = 2π r / v = 2π(1.22 × 10⁹) ÷ 5.57 × 10³ = 1.376 × 10⁶ s = 15.9 days.

Marking: (a) 1 for the equation, 1 for the value; (b) 1 for the value.

Question 5 Vertical circle (3 marks)

T + m g = m v² / r (both forces point down toward the centre).
T = m(v² / r − g) = 0.30 × (20 − 9.81) = 3.1 N.
T − m g = m v² / r, so T = 0.30 × (31.25 + 9.81) = 12 N.

Marking: 1 mark per part.

Question 6 Outward force argument (3 marks)

The claim is incorrect. If the forces were balanced, the net force would be zero and the Moon would move in a straight line. The only significant force is the Earth’s gravity, which is unbalanced and gives a centripetal acceleration v² / r toward the Earth. The Moon does fall toward the Earth all the time, but its sideways velocity means the Earth’s surface curves away beneath it, so the distance stays almost constant.

Marking: 1 mark for rejecting the balanced-force claim, 1 for stating that gravity is the net centripetal force, 1 for linking the sideways velocity to continuous falling.