Paper 3 Circular Motion Drills

Q1 Conical pendulum

A small bob of mass $0.080\mathrm{kg}$ moves in a horizontal circle as a conical pendulum. The string length is $0.90\mathrm{m}$ and makes an angle of $22^{\circ }$ with the vertical.

1. Draw or describe the forces on the bob. [2]
2. Calculate the radius of the circular path. [2]
3. Use vertical equilibrium and horizontal circular motion to show that

$${\omega }^2=\frac{g}{L\cos \theta }.$$

[4] 4. Calculate the period of the motion. [3] 5. Explain why the bob’s acceleration is not in the direction of the string. [2]

Q2 Circular motion from known force

A model aircraft of mass $0.75\mathrm{kg}$ flies in a horizontal circle of radius $18\mathrm{m}$. The horizontal component of lift available for turning is $9.0\mathrm{N}$.

1. Explain the analysis path from known force to motion quantity. [2]
2. Calculate the centripetal acceleration. [2]
3. Calculate the maximum speed for this circular path. [3]
4. Calculate the angular speed at this speed. [2]
5. State what happens if the aircraft tries to fly faster without increasing the inward resultant force. [2]