Originally Posted by

**Wonkihead** I have a worksheet with answers missing. The questions are simple uniform motion in a circle ones but I would like to run through two of them here and just have you more experienced folks confirm my answers, if you wouldn't mind.

**Question 1**

Find the speed of a particle of dust, 5cm from the center of a disc which is revolving at 45rpm. Also find the acceleration of the particle. Answers to 2 decimal places.

*Answer:*

$\displaystyle

\omega = 45\text{ rpm}

= \frac{45(360)}{60} \text{ deg s}^{-1}

= \frac{45(360)(\pi)}{60(180)} \text{ rad s}^{-1}

= \frac{3}{2}\pi \text{ rad s}^{-1}

$

For the speed of the particle

$\displaystyle

v = r\omega

= 0.05\bigg(\frac{3}{2}\pi\bigg)

= { \color{blue}0.34 \text{ ms}^{-1} } \text{ (2 d.p.)}

$

For the acceleration of the particle

$\displaystyle

a = r\omega^2

= 0.05\bigg(\frac{3}{2}\pi\bigg)^2

= {\color{blue}1.11 \text{ ms}^{-2} } \text{ (2 d.p.)}

$

**Question 2**

A particle P of mass 20 grams is connected by a taut inextensible string of length 2m to a fixed point O of a smooth horizontal table on which the particle rests. The string will break if the tension exceeds 7.84N. Calculate the greatest possible speed at which P can describe a circle of 2m about O.

*Answer:*

$\displaystyle \text{mass, } m = 0.02 \text{ kg}$

For a maximum string tension of 7.84N

$\displaystyle F = ma$

$\displaystyle 7.84 = 0.02a$

$\displaystyle a = 392 \text{ ms}^{-2}$

For the speed

$\displaystyle v^2 = ra^2$

$\displaystyle v = \sqrt{ 2(392)^2 }$

$\displaystyle v = {\color{blue}554.37 \text{ ms}^{-1} } \text{ (2 d.p.)}$

Thanks!