Answer:
θ= 555.55 rad
Explanation:
Newton's second law:
F = ma has the equivalent for rotation:
τ = I * α Formula (1)
where:
τ : It is the moment applied to the body. (Nxm)
I : moment of inertia: it is the moment of inertia of the body with respect to the axis of rotation (kg*m²)
α : It is angular acceleration. (rad/s²)
Moment of inertia of the disc that rotates around an axis through its center
I= (1/2) m*R² Formula (2)
Where:
m:mass of the disc (kg)
R: radius of the disc (m)
Torque applied to disc (τ)
τ = F*R Formula (3)
Where
F: tangential force applied to the disc
R :Distance from F to the axis of rotation (m)
Data
m : 12 kg
R = 30 cm= 0.3 m
F= 80 N
Problem Development
We replace Formula (2) and Formula (3) in the formula (1)
τ = I * α
F*R= (1/2) m*R²* α
α = [tex]\alpha = \frac{F*R}{\frac{1}{2}*m*R^{2} }[/tex]
[tex]\alpha =\frac{2F}{m*R}[/tex]
[tex]\alpha =\frac{2*80}{12*0.3}[/tex]
α = 44.4 rad/s²
Kinematics of the disc
We apply the equations of circular motion uniformly accelerated
θ= ω₀ t+ (1/2)α*t² Formula (4)
Where:
α : Angular acceleration (rad/s²)
ω₀ : Initial angular speed ( rad/s)
t: time interval (s)
θ : Angle that the body has rotated in a given time interval (rad)
Data
ω₀= 0
α = 44.4 rad/s²
t =5 s
We replace data in the formula (4)
θ= 0+ (1/2)(44.4)*(5)²
θ= 555.55 rad
