Paper 4 Circular Motion Answers

Q1 Whirling bung experiment

1. The reaction-time uncertainty is roughly the same for one timing action, but the measured time is much larger for many revolutions, so percentage uncertainty in period is reduced. [2]
2. $T=t/N$. [1]
3. $v=2\pi r/T$. [1]
4. Use a fixed marker below the tube; keep the marker just below the tube during rotation; practise maintaining steady motion; measure radius from centre of circle to centre of bung. [2]
5. Wear eye protection, keep clear space around the rotating bung, check the string is secure, or use a soft bung. [1]

Q2 Testing $a_c=r{\omega }^2$

1. Correct values of ${\omega }^2$ from $2.25$ to $16.0\mathrm{ra}{\mathrm{d}}^2{\mathrm{s}}^{-2}$. [1]
2. Axes and units [1]; suitable scale [1]; accurate plots [2]; best-fit straight line [1]. [5]

3. The best-fit gradient is approximately $0.239\mathrm{m}$, since

$$a=r{\omega }^2.$$

Hence $r\approx 0.239\mathrm{m}$. Accept a value consistent with the candidate’s line. [3] 4. The fitted intercept is about $0.016\mathrm{m}{\mathrm{s}}^{-2}$, small compared with the measured accelerations and close to zero within realistic experimental uncertainty; the model is therefore supported. [2] 5. Sensor zero offset, imperfect levelling, vibration, or imperfect identification of the rotation axis. [1] 6. Slipping changes $r$ and invalidates the data; detachment also makes the sensor a projectile and creates a safety hazard. [1]