Question

The track of a gramophone record is the shape of a spiral curve and may be considered as a number of concentric circles of inner and outer radius 5.25cm and 10.5cm respectively. The record rotates at 33 and 1/3 revs/min and takes 18 minutes to play. Find the length of the track.

Answer 1

Circumference of track C is found from the following:\[C=\pi d\]where d is the diameter.
The average diameter of tracks d(av) is found as follows:
\[d(av)=\frac{5.25\times 2+10.5\times 2}{2}=\frac{31.5}{2}cm\]
The average circumference C(av) is as follows:
\[C(av)=\pi \times \frac{31.5}{2}\]
Total number of revolutions to play the record R(total) is found from the following:
\[R(total)=33\frac{1}{3}\times 18=\frac{100\times 18}{3}\]
The total length of the track Len(total) is found by multiplying the average circumference of one track by the toal number of revolutions as follows:
\[Len(total)=\frac{100\times 18\times \pi \times31.5}{3\times 2}=?cm\]

Answer 2

thanks