Explanation:
Given that phonograph rotates 33.5 times per minute:
Frequency of the phonograph = [tex]33.5 min^{-1}[/tex]
Time period =[tex]\frac{1}{frequency}=\frac{1}{33.5 min^{-1}}=0.0298 min[/tex]
time period = 0.0298 × 60 seconds =1.788 seconds
Radius r = 15 cm = 0.15 m (1 m = 100 cm)
The linear speed =[tex]\frac{Distance}{time}=\frac{2\pi\times r}{1.788 sec}=\frac{2\times 3.14\times 0.15 m}{1.788 sec}=0.526 m/s[/tex]
The centripetal acceleration of a point on its rim:
[tex]\frac{(\text{linear velocity})^2}{\text{radius of the rim}}=\frac{(0.526 m/s)^2}{0.15 m}=1.84 m/s^2[/tex]
Centripetal acceleration is [tex]1.84 m/s^2[/tex].
