NJC 2022 Motion in a Circle Problems Set

National Junior College 2022 | SH1 | H2 Physics Motion In a Circle - Problem Set Exercises Kinematics of Uniform Circular Motion E1. What is 𝜋 4 𝑟𝑎𝑑 in degrees? [45°] 𝜋/4 2𝜋 × 360° E2. What is 300° in radians? [5.23 rad] 5 3 𝜋 = 5.23 radians E3. (2020 P1 Q11) [B] 𝜔 = 2𝜋 𝑇 = 2𝜋 60×60 = 1.75 × 10−3 𝑟𝑎𝑑 𝑠−1 E4. (2016 P1 Q12) [D] 𝜔 = 2𝜋 𝑇 = 2𝜋 24×60×60 = 7.27 × 10−5 𝑟𝑎𝑑 𝑠−1

National Junior College 2022 | SH1 | H2 Physics E5. Assuming that the earth moves in a circle at a constant rate around the sun, calculate the angular velocity of the earth around the sun. (Hint: how long does it take for the earth to go round the sun once?) [1.99 × 10−7𝑟𝑎𝑑 𝑠−1] 2𝜋 365×24×60×60 = 1.99 × 10−7𝑟𝑎𝑑 𝑠−1 (The earth takes 365 days to go round the sun. The earth takes 24 hours to rotate about its own axis which results in the day and night cycle.) E6. A car is moving around a circular track of radius 400 𝑚 at constant angular velocity 0.050 𝑟𝑎𝑑 𝑠−1. Calculate the total distance the car moves in 5 minutes. [6000 m] Angular displacement in 5 min = 𝜔𝑡 = 0.05 × 5 × 60 = 15 𝑟𝑎𝑑 Distance moved in 5 min = 𝑟𝜃 = 15 × 400 = 6000 𝑚 E7. A rod is made to spin at a constant rate of 3 complete revolutions per second as shown below. What is the difference in angle between the rod’s current position and its position 0.50 seconds later? [𝜋 𝑟𝑎𝑑] Angular displacement in 0.50 s = 𝜔𝑡 = 3×2𝜋 1 × 0.50 = 3𝜋 The rod would have moved 1.5 complete circles. Hence the difference in angle = 3𝜋 − 2𝜋 = 𝜋 𝑟𝑎𝑑 = 3.14 𝑟𝑎𝑑 E8. (2017 P1 Q9) D (both have the same angular velocity, hence angular displacement will be the same, although actual distance travelled will be larger for P)

National Junior College 2022 | SH1 | H2 Physics Centripetal Force E9. The diagram shows a child sitting on a playground turntable, which is turning with constant angular velocity. Which diagram shows the forces acting on the child when in the position shown? A (centripetal force is a resultant force) E10. (2013 P1 Q11) B (The tension and weight result in a centripetal force to the left pointing to the center of the horizontal circle)

National Junior College 2022 | SH1 | H2 Physics Problems Kinematics of Uniform Circular Motion P1. A body rotates with uniform speed in a circle of radius 𝑟 and takes time 𝑇 to complete one revolution. What are the magnitudes of the angular velocity 𝜔, the linear velocity 𝑣, and the acceleration 𝑎? angular velocity 𝜔 linear velocity 𝑣 acceleration 𝑎 A 1 𝑇 4𝜋𝑟 𝑇 2𝜋𝑟 𝑇2 B 2𝜋 𝑇 2𝜋𝑟 𝑇 2𝜋𝑟 𝑇2 C 2𝜋 𝑇 2𝜋𝑟 𝑇 4𝜋2𝑟 𝑇2 D 2𝜋 𝑇 4𝜋𝑟 𝑇 4𝜋2𝑟 𝑇2 C (𝑣 = 𝑟𝜔, 𝑎 = 𝜔2𝑟) P2. (2017 P1 Q9) D (𝜔 is the same for both points 𝑎 = 𝜔2𝑟 Since radius is halved, the centripetal acceleration is also halved to 8 cm s-2)

National Junior College 2022 | SH1 | H2 Physics P3. (2020 P1 Q10) B (𝑎 = 𝜔2𝑟 = 4𝜋2 (27.3×24×60×60)2 × 3.85 × 108 = 2.73 × 10−3 𝑚𝑠−2) P4. Singapore is on the equator. Cambridge is at a latit