Answer:
a. ω₂ = 14rad/s
b. ∇K.E = 0.014J
c. The bug does not conserve force while moving on the disk (non-conservative force).
Explanation:
Mass of the bug (m) = 0.02kg
Mass of the cylindrical disk (M) = 0.10kg
Radius of the disk (r) = 0.10m
Initial angular velocity ω₁ = 10rad/s
final angular velocity ω₂ = ?
a.
To calculate the new angular velocity, we relate it to the conservation of angular momentum of the system I.e when the bug was at the edge of the disk and when it is located at the centre of the disk.
I = Mr² / 2
I₁ = Mr₂ / 2 + mr²
I₁ = moment of inertia when the bug was at the edge
I₁ = [(0.10 * 0.10²) / 2 ] + (0.02 * 0.1²)
I₁ = 0.0005 + 0.0002
I₁ = 7.0*10⁻⁴kgm²
I₂ = moment of inertia when yhe bug was at the center of the disk.
I₂ = Mr² / 2
I₂ = (0.01 * 0.01²) 2
I₂ = 0.0005kgm²
for conservation of angular momentum,
I₁ω₁ = I₂ω₂
solve for ω₂
ω₂ = (I₁ * ω₁) / I₂
ω₂ = (7.0*10⁻⁴ * 10) / 5.0*10⁻⁴
ω₂ = 14 rad/s
b. the change in kinetic energy of the system is
∇K = K₂ - K₁
∇K = ½I₂*ω₂² - ½I₁*ω₁²
∇K = ½(I₂*ω₂² - I₁ω₁²)
∇K = ½[(5.0*10⁻⁴ * 14²) - (7.0*10⁻⁴ * 10²)]
∇k = ½(0.098 - 0.07)
∇K = ½ * 0.028
∇K = 0.014J
c.
The cause of the decrease and increase in kinetic energy is because the bug uses a non-conservative force. To conserve the mechanical energy of a system, all the forces acting in it must be conservative.
The work W produced by this force brings the difference in kinetic energy of the system
W = K₂ - K₁
