Respuesta :
Answer:
57.6Joules
Explanation:
Rotational kinetic energy of a body can be determined using the expression
Rotational kinetic energy = 1/2Iω²where;
I is the moment of inertia around axis of rotation. = 5kgm/s²
ω is the angular velocity = ?
Note that torque (T) = I¶ where;
¶ is the angular acceleration.
I is the moment of inertia
¶ = T/I
¶ = 3.0/5.0
¶ = 0.6rad/s²
Angular acceleration (¶) = ∆ω/∆t
∆ω = ¶∆t
ω = 0.6×8
ω = 4.8rad/s
Therefore, rotational kinetic energy = 1/2×5×4.8²
= 5×4.8×2.4
= 57.6Joules
Given Information:
Torque = τ = 3.0 N.m
Moment of inertia = I = 5.0 kg.m²
Time = t = 8 seconds
Required Information:
Rotational kinetic energy = Erot = ?
Answer:
Rotational kinetic energy = 57.6 Joules
Explanation:
We know that the rotational kinetic energy of the wheel is the energy due to its rotation and is part of its total kinetic energy and is given by
Erot = ½Iω²
Where ω is the angular velocity and I is the moment of inertia of the wheel.
We also know the relation between torque and moment of inertia is
τ = Iα
Where α is the angular acceleration of the wheel.
α = τ/I
From the equations of kinematics, we know that final angular velocity is given by
ω = ω₀ + αt
Where ω₀ is the initial angular velocity of the wheel and since wheel starts from rest, ω₀ is zero.
ω = 0 + αt
ω = αt
ω = (τ/I)t
ω = τ*t/I
Finally the equation of rotational kinetic energy becomes
Erot = ½Iω²
Erot = ½I(τ*t/I)²
Erot = ½*5*((3*8)/5)²
Erot = ½*5*(23.04)
Erot = ½*(115.2)
Erot = 57.6 J
Therefore, the wheel's rotational kinetic energy at the end of 8 s is 57.6 Joules.
