Answer:
A) τ = 300 N*m
B) θ = 0.4 rad = 22.9°
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 : 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)
Data
I = 0.6 kg*m² : moment of inertia of the bat
Angular acceleration of the bat
We apply the equations of circular motion uniformly accelerated :
ωf= ω₀ + α*t Formula (2)
Where:
α : Angular acceleration (rad/s²)
ω₀ : Initial angular speed ( rad/s)
ωf : Final angular speed ( rad
t : time interval (s)
Data
ω₀ = 0
ωf = 20 rad/s
t = 40 ms = 0.04 s
We replace data in the formula (2) :
ωf= ω₀ + α*t
20 = 0 + α* (0.04)
α = 20/ (0.04)
α = 500 rad/s²
Newton's second law to the bat
τ = (0.6 kg*m²) *(500 rad/s²) = 300 (kg*m/s²)* m
τ = 300 N*m
B) Angle through which the bat moved.
We apply the equations of circular motion uniformly accelerated :
ωf²= ω₀ ²+ 2α*θ Formula (3)
Where:
θ : Angle that the body has rotated in a given time interval (rad)
We replace data in the formula (3):
ωf²= ω₀²+ 2α*θ
(20)²= (0)²+ 2(500 )*θ
400 = 1000*θ
θ = 400/1000
θ = 0.4 rad
π rad = 180°
θ = 0.4 rad *(180°/π rad)
θ = 22.9°
