Answer:
[tex]124.62\ \text{rad/s}[/tex]
[tex]3.71\ \text{m/s}[/tex]
[tex]1.23\ \text{km/s}^2[/tex]
[tex]20.28\ \text{m}[/tex]
Explanation:
r = Radius of disk = 7.9 cm
N = Number of revolution per minute = 1190 rev/minute
Angular speed is given by
[tex]\omega=N\dfrac{2\pi}{60}\\\Rightarrow \omega=1190\times \dfrac{2\pi}{60}\\\Rightarrow \omega=124.62\ \text{rad/s}[/tex]
The angular speed is [tex]124.62\ \text{rad/s}[/tex]
r = 2.98 cm
Tangential speed is given by
[tex]v=r\omega\\\Rightarrow v=2.98\times 10^{-2}\times 124.62\\\Rightarrow v=3.71\ \text{m/s}[/tex]
Tangential speed at the required point is [tex]3.71\ \text{m/s}[/tex]
Radial acceleration is given by
[tex]a=\omega^2r\\\Rightarrow a=124.62^2\times 7.9\times 10^{-2}\\\Rightarrow a=1226.88\approx 1.23\ \text{km/s}^2[/tex]
The radial acceleration is [tex]1.23\ \text{km/s}^2[/tex].
t = Time = 2.06 s
Distance traveled is given by
[tex]d=vt\\\Rightarrow d=\omega rt\\\Rightarrow d=124.62\times 7.9\times 10^{-2}\times 2.06\\\Rightarrow d=20.28\ \text{m}[/tex]
The total distance a point on the rim moves in the required time is [tex]20.28\ \text{m}[/tex].
