Answer:
T = 0.01 Nm
Explanation:
First, we will calculate the angular acceleration of the disk:
[tex]2\theta\alpha = \omega_f^2-\omega_i^2[/tex]
where,
θ = angular displacement = (6.37 rev)(2π rad/1 rev) = 40.02 rad/s
α = angular acceleration = ?
ωi = initial angular speed = 10 rad/s
ωf = final angular speed = 0 rad/s
Therefore,
[tex](2)(40.02\ rad/s)\alpha = (0\ rad/s)^2-(10\ rad/s)^2[/tex]
α = -1.25 rad/s²
negative sign shows deceleration
α = 1.25 rad/s²
Now, we will calculate the moment of inertia of disk:
[tex]I = \frac{1}{2}mr^2[/tex]
where,
I = Moment of Inertia = ?
m = mass of disk = 1 kg
r = radius of disk = 0.13 m
Therefore,
[tex]I = \frac{1}{2} (1\ kg)(0.13\ m)^2[/tex]
I = 0.00845 kg.m²
Now, the torque can be given as:
T = Iα
T = (0.00845 kg.m²)(1.25 rad/s²)
T = 0.01 Nm
