JPJC 2026 Circular Motion Tutorial

2026/JPJC/PHYSICS/9478 1 JURONG PIONEER JUNIOR COLLEGE 9478 H2 PHYSICS CIRCULAR MOTION TUTORIAL Self-Check Questions S1 Define angular displacement and angular velocity. S2 Define one radian. S3 Define the frequency of a circular motion. Self-Practice Questions P1 Calculate the angular velocities of the second, minute and hour hands of the clock. P2 A record on a turntable is rotating at a constant number of revolutions per second. State the equation relating the tangential speed v of a point on the record and its distance r from the centre of rotation, and sketch the graph of v against r. P3 A communications satellite of mass m moves at constant angular speed  in a circular orbit of radius r about the Earth’s centre of mass. Determine the work done on the satellite in one revolution? Explain your answer. P4 An object is moving in a uniform circular motion. Explain (a) why the object experiences acceleration and (b) why the acceleration is perpendicular to the direction of motion. Discussion Questions 1 A rubber ball of mass 0.12 kg is whirled round a horizontal circle on the end of a string of length 0.80 m and completes 7.0 revolutions per second. Calculate (a) its angular velocity, (b) its speed, (c) its acceleration, (d) the centripetal force acting on the object. 2 A car of mass 1000 kg is travelling round a bend at 20 m s−1. (a) If the limiting friction between the tyres and the road is 6000 N, calculate the smallest radius the car can travel at. (b) If there were no friction between the tyres and the road, calculate the angle the bend should be banked in order to maintain this radius of movement. 3 An airplane travelling at 360 km h−1 is attempting to make a horizontal turn with a radius of curvature of 5.0 km. Calculate the angle at which the pilot should bank his airplane.

2026/JPJC/PHYSICS/9478 2 4 An aircraft is trave lling at a constant speed of 180 m s−1 in a horizontal circle of radius 20 km. A plumbline, attached to the roof of the cabin, settles at an angle  to the true vertical while the aircraft is turning. (a) Calculate the acceleration of the aircraft. (b) Draw a labelled force diagram to show the directions of the forces acting on the bob of the plumbline. Indicate the centre of the circle in your sketch. (c) Calculate the angle  . 5 A model airplane of mass 0.75 kg is flying at constant speed in a horizontal circle at one end of a 30 m cord and at a height of 18 m. The other end of the cord is tethered to the ground. The airplane circles 4.4 rounds per minute and has its wings horizontal, with the air pushing vertically upward. Calculate (a) the acceleration of the plane, (b) the tension in the cord, (c) the total upward force (lift) on the plane’s wings. 6 TYS 2018 P2 Q2 7 A small ball of mass m is fixed to one end of a light rigid rod. The ball is made to move at constant speed around the circumference of a vertical circle with centre at C, as shown in the diagram. When the rod is vertical with the ball above C, the tension T in the rod is given by 2T mg= , where g is the acceleration of free fall. (a) (i) Explain why the centripetal force on the ball is greater than 2mg. (ii) State, in terms of mg, the magnitude of the centripetal force. (iii) Determine the magnitude of the tension, in terms of mg, in the rod when the rod is vertical, with the ball below point C. (b) The distance from the centre of the ball to point C is 0.72 m. Use your answers in (a)(ii) to determine, for the ball, (i) the angular speed, (ii) the linear speed. (c) The ball has a constant angular speed. (i) Explain why work has to be done for the ball to move from the position where it is vertically above point C to the position where it is vertically below C. (ii) Calculate the work done in (i) for a ball of mass 240 g. 0.72 m C ball, mass m light rod

2026/JPJC/PHYSICS/9478 3 Challenging Question 8 A stone of mass 500 g is attached to a string of length 50 cm which will break if the tension exceeds 20 N. The stone is whirled in a vertical circle, with the centre of the axis of rotation being at a height 100 cm above the ground. (a) The angular velocity is slowly increased until the string breaks. Predict the position in the circular motion at which the string is most likely to break. (b) Calculate the angular velocity at which this break first occurs. (c) Hence, calculate the horizontal displacement of the stone before it hits the ground. (d) Explain whether it is possible for the stone moving in a vertical circle to truly experience uniform circular motion in real life? [Hint: Think about the stone at different points in the circle.] Answers: P1 0.105 rad s−1, 31.75 10 − rad s−1, 41.45 10 − rad s−1 1 (a) 44 rad s−1 (b) 35 m s−1 (c) 1500 m s−2 (d) 190 N 2 (a) 67 m (b) 31° 3 12° 4 (a) 1.6 m s−2 (c) 9.4° from true vertical 5 (a) 5.1 m s−2 (b) 4.8 N (c) 10 N 6 (b) 0.29 J (c) 2.4 m s−1 (d) 1.4 m s−1 7 (a)(ii) 3mg (iii) 4mg (b)(i) 6.4 rad s−1 (ii) 4.6 m s−1 (c)(ii) −3.4 J 8 (b) 7.8 rad s−1 (c) horizontal displacement of 1.2 m from breaking point