Consider that the period is given by the following expression:
[tex]T=\frac{1}{f}[/tex]
where,
f: angular frequency = 33 1/3 rpm = 100/3 rpm
Convert 100/3 rpm to rev/s:
[tex]\frac{100}{3}\text{rpm}=\frac{100}{3}\frac{\text{rev}}{\min}\cdot\frac{1\min }{60s}=\frac{100}{180}\frac{\text{rev}}{s}=\frac{5}{9}\frac{\text{rev}}{s}[/tex]
Next, replace the previous values of w into the formula for T:
[tex]T=\frac{1}{\frac{5}{9}\frac{\text{rev}}{s}}=\frac{9}{5}s\approx1.80s[/tex]
Hence, the period of the record is 1.80s
