Paper 4 Circular Motion Drills

Q1 Whirling bung experiment

A student whirls a rubber bung in a horizontal circle of radius $r$. The time for $N$ revolutions is measured.

1. Explain why timing many revolutions is better than timing one revolution. [2]
2. State how the period $T$ is found from the measured time. [1]
3. State how the speed $v$ of the bung is calculated from $r$ and $T$. [1]
4. Suggest two precautions for keeping the radius constant. [2]
5. State one safety precaution. [1]

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

A small acceleration sensor is fixed to a rotating turntable. Its distance $r$ from the rotation axis is constant. The measured centripetal acceleration $a$ is shown below.

$\omega /\mathrm{rad}{\mathrm{s}}^{-1}$	$a/\mathrm{m}{\mathrm{s}}^{-2}$
1.50	0.56
2.00	0.96
2.50	1.52
3.00	2.19
3.50	2.91
4.00	3.86

1. Calculate ${\omega }^2$ for each reading. [1]
2. Plot $a$ against ${\omega }^2$ and draw a best-fit straight line. [5]

3. Use the gradient to determine $r$. [3]
4. Comment on whether the intercept supports the model $a=r{\omega }^2$. [2]
5. Suggest one reason for a small non-zero intercept. [1]
6. State one reason why the sensor must be securely attached to the turntable. [1]