The angular speed of the ball as it swings through its lowest point is 1.8 rad/s.
The given parameters;
radius of the circular path, r = 2.5 m
angle with the vertical, θ = 35⁰
The angular speed of the ball, as it swings through its lowest point is calculated as follows;
[tex]Tcos \theta = m\omega ^2 r\\\\mgcos \theta = m \omega ^2 r\\\\gcos \theta = \omega ^2 r\\\\\omega ^2 = \frac{gcos \theta }{r} \\\\\omega = \sqrt{\frac{gcos \theta }{r} } \\\\\omega = \sqrt{\frac{9.8 \times cos (35) }{2.5} } \\\\\omega = 1.8 \ rad/s[/tex]
Thus, the angular speed of the ball as it swings through its lowest point is 1.8 rad/s.
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