Answer:
The angular speed of rotation is 1.34 rad/s.
Explanation:
Given that,
Length = 3.40 m
Distance = 5.90 m
Angle = 45.0°
We need to calculate the angular speed of rotation
Using balance equation
Horizontal component
[tex]T\cos\theta=mg[/tex]
[tex]T=\dfrac{mg}{\cos\theta}[/tex]
Vertical component
[tex]T\sin\theta=m\omega^2 r[/tex]
Put the value of T
[tex]mg\tan\theta=m\omega^2(d+L\sin\theta)[/tex]
[tex]\omega=\sqrt{\dfrac{g\tan\theta}{(d+L\sin\theta)}}[/tex]
Put the value into the formula
[tex]\omega=\sqrt{\dfrac{9.8\tan45.0}{5.90+3.40\sin45.0}}[/tex]
[tex]\omega=1.34\ rad/s[/tex]
Hence, The angular speed of rotation is 1.34 rad/s.
