Answer:
Explanation:
Given,
Angular displacement, θ = 3 rev
= 3 x 2π = 6π
initial angular speed, ω = 0 rad/s
Angular speed when disk is revolved to 3 revolution = 6 rad/s
radius, r = 1.2 m
time, t = 20 s
Calculating angular acceleration
[tex]\omega^2 = \omega_0^2 +2 \alpha \theta[/tex]
[tex](6)^2= 0 +2 \alpha\times (6\pi)[/tex]
[tex]\alpha = 0.955\ rad/s^2[/tex]
Acceleration of the disk
[tex]a = \alpha R[/tex]
[tex]a =0.955\times 1.2 = 1.146\ m/s^2[/tex]
Now for linear velocity calculation
[tex]\omega = \omega_0 + \alpha t[/tex]
[tex]\omega =0 +0.955\times 20[/tex]
[tex]\omega = 19.1\ rad/s[/tex]
Linear velocity,
[tex]v = r \omega[/tex]
[tex]v = 1.2 \times 19.1[/tex]
[tex]v = 22.92\ m/s[/tex]
