33 1/3 rpm can be written as follow;
[tex]33\frac{1}{3}\text{rpm}=\frac{100}{3}rpm[/tex]The period is given by:
[tex]T=\frac{2\pi}{\omega}[/tex]where w = 100/3 rpm is the angular frequency. Convert 100/3 rpm to rev/s, as follow:
[tex]\frac{100}{3}\frac{\text{rev}}{\min}\cdot\frac{1\min }{60s}=0.555\frac{rev}{s}[/tex]By replacing into the formula for the period T you obtain:
[tex]T=\frac{2\pi}{0.555\frac{\text{rev}}{s}}\approx11.3s[/tex]Hence, the period is approximately 11.3s
