The rotational speed of a 33 rpm record is
[tex]\omega = (33 \, \frac{rev}{min} )*( \frac{1 \, min}{60 \, s})*(2 \pi \, \frac{rad}{rev} ) = 3.4558 \, rad/s[/tex]
The angle swept in 0.27 s is
[tex]\theta = (3.4558 \, \frac{rad}{s})*(0.27 \, s) = 0.933 \, rad[/tex]
In degrees,
0.933 rad = (0.933/π)*180 = 53.5°
Answer: 53.5°
