Answer:
10.84406 Nm/rad
0.068625 kgm²
2.00066 rad/s
0.49983 s
Explanation:
F = Force = 4.29 N
R = Radius = [tex]\dfrac{30}{2}=15\ cm[/tex]
[tex]\theta[/tex] = Angle = [tex]3.4\ ^{\circ}[/tex]
m = Mass of disk = 6.1 kg
Torsional constant is given by
[tex]J=\dfrac{\tau}{\theta}\\\Rightarrow J=\dfrac{FR}{\theta}\\\Rightarrow J=\dfrac{4.29\times 0.15}{3.4\times \dfrac{\pi}{180}}\\\Rightarrow J=10.84406\ Nm/rad[/tex]
The torsion constant is 10.84406 Nm/rad
Moment of inertia is given by
[tex]I=\dfrac{1}{2}mr^2\\\Rightarrow I=\dfrac{1}{2}6.1\times 0.15^2\\\Rightarrow I=0.068625\ kgm^2[/tex]
The moment of inertia is 0.068625 kgm²
Frequency is given by
[tex]f=\dfrac{1}{2\pi}\sqrt{\dfrac{J}{I}}\\\Rightarrow f=\dfrac{1}{2\pi}\sqrt{\dfrac{10.84406}{0.068625}}\\\Rightarrow f=2.00066\ rad/s[/tex]
The frequency is 2.00066 rad/s
Time period is given by
[tex]T=\dfrac{1}{f}\\\Rightarrow T=\dfrac{1}{2.00066}\\\Rightarrow T=0.49983\ s[/tex]
The time period is 0.49983 s
