4C.1.1 Angular speed and conical pendulum motion Quiz: Pearson Edexcel Further Maths, Unit 30

The 20 questions

1. What is the relation between linear speed v, radius r and angular speed omega for uniform circular motion?

   • v = omega / r
   • v = r / omega
   • omega = r v
   • v = r omega

2. What is the radial acceleration of a particle moving in a horizontal circle of radius r with speed v and angular speed omega?

   • r^2 omega^2
   • r omega
   • v^2/r, which equals r omega^2
   • v/r

3. In which direction does the radial acceleration of a particle in uniform circular motion act?

   • Away from the centre of the circle
   • Tangent to the circle
   • Towards the centre of the circle
   • Along the direction of the velocity

4. For a conical pendulum with string at angle theta to the vertical, which equation holds vertically?

   • T = m g
   • T cos(theta) = m r omega^2
   • T sin(theta) = m g
   • T cos(theta) = m g

5. For a conical pendulum, which equation gives the horizontal motion?

   • T sin(theta) = m g
   • T sin(theta) = m r omega^2
   • T cos(theta) = m r omega^2
   • T = m r omega

6. What are the units of angular speed?

   • revolutions per metre
   • seconds per radian
   • radians per second, rad s^-1
   • metres per second

7. What is the period of motion of a particle with angular speed omega in a circle?

   • 1 / omega
   • 2 pi omega
   • 2 pi / omega
   • omega / (2 pi)

8. A conical pendulum has string length L = 1.25 m, angle theta with cos(theta) = 0.8, mass 0.4 kg and g = 10 m/s^2. What is the angular speed, to 2 decimal places?

   • 3.16 rad/s
   • 1.58 rad/s
   • 4.00 rad/s
   • 10.0 rad/s

9. For the conical pendulum above, what is the speed of the bob, to 2 decimal places?

   • 1.25 m/s
   • 3.16 m/s
   • 2.37 m/s
   • 5.00 m/s

10. For the same conical pendulum, what is the tension in the string?

    • 5 N
    • 6.25 N
    • 4 N
    • 3.2 N

11. For the same conical pendulum, what is the radial acceleration of the bob?

    • 5.63 m/s^2
    • 3.16 m/s^2
    • 7.5 m/s^2
    • 10 m/s^2

12. A particle moves in a horizontal circle of radius 0.3 m at 2 revolutions per second. What is its angular speed, to 2 decimal places?

    • 6.28 rad/s
    • 2 rad/s
    • 12.57 rad/s
    • 25.13 rad/s

13. A conical pendulum has L = 0.5 m, string angle 60 degrees to the vertical, and g = 10 m/s^2. What is the angular speed, to 2 decimal places?

    • 20.0 rad/s
    • 4.47 rad/s
    • 6.32 rad/s
    • 3.16 rad/s

14. A conical pendulum has angular speed 3.16 rad/s. What is its period, to 2 decimal places?

    • 6.28 s
    • 3.16 s
    • 1.99 s
    • 0.50 s

15. A particle moves in a horizontal circle of radius 0.6 m with speed 3 m/s. What is its radial acceleration?

    • 5 m/s^2
    • 1.8 m/s^2
    • 9 m/s^2
    • 15 m/s^2

16. A conical pendulum has L = 0.8 m, string angle 60 degrees to the vertical and g = 10 m/s^2. What is the angular speed?

    • 3.54 rad/s
    • 5 rad/s
    • 25 rad/s
    • 2.50 rad/s

17. A conical pendulum of mass 0.4 kg has string angle 60 degrees to the vertical and g = 10 m/s^2. What is the tension?

    • 8 N
    • 6.93 N
    • 4 N
    • 3.46 N

18. A conical pendulum has depth h = 0.36 m below its pivot, with g = 10 m/s^2. Using omega^2 = g/h, what is the angular speed, to 2 decimal places?

    • 27.8 rad/s
    • 2.73 rad/s
    • 3.00 rad/s
    • 5.27 rad/s

19. A bob of mass 2 kg on a string of length 1 m moves in a conical pendulum at 30 degrees to the vertical, with g = 10 m/s^2. What is its speed, to 2 decimal places?

    • 1.70 m/s
    • 5.00 m/s
    • 0.58 m/s
    • 2.89 m/s

20. For a conical pendulum with fixed L and mass, what happens to the string angle when the angular speed is doubled?

    • cos(theta) falls to one quarter of its old value, so the string moves towards the horizontal
    • The angle is unchanged, since the mass is fixed
    • cos(theta) doubles, so the string moves towards the vertical
    • The string moves towards the vertical

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