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A flywheel with a radius of 0.600 m starts from rest and accelerates with a constant angular acceleration of 0.200 rad/s2 . Part A: Compute the magnitude of the tangential acceleration of a point on its rim at the start.; Part B: Compute the magnitude of the radial acceleration of a point on its rim at the start.; Part C: Compute the magnitude of the resultant acceleration of a point on its rim at the start.; Part D: Compute the magnitude of the tangential acceleration of a point on its rim after it has turned through 60.0 ∘; Part E: Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 60.0 ∘.; Part F: Compute the magnitude of the resultant acceleration of a point on its rim after it has turned through 60.0 ∘.; Part G: Compute the magnitude of the tangential acceleration of a point on its rim after it has turned through 120.0 ∘.; Part H: Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 120.0 ∘.; Part I: Compute the magnitude of the resultant acceleration of a point on its rim after it has turned through 120.0 ∘.



Answer :

Part A:

Radius of flywheel = 0.600 m

Angular acceleration of flywheel (αₐ) = 0.200 rad/s²

The tangential acceleration of a point at the start (αₓ) =

= αₓ = αₐ × r

= αₓ = 0.200 × 0.600

= αₓ = 0.12 m/s²

Part B:

Radius of flywheel = 0.600 m

Angular acceleration of flywheel (αₐ) = 0.200 rad/s²

Angular speed = ω = 0 m/s²

Magnitude of radial acceleration of a point on rim at the start (αₙ)=

= (angular speed)² × r

= 0 × 0.600

= 0 m/s²

Part C:

Radius of flywheel = 0.600 m

Angular acceleration of flywheel (αₐ) = 0.200 rad/s²

Resultant acceleration of a point on the rim at the start =

= α =√(αₙ² + αₓ²)

= α = √ (0² + 0.12²)

= α = 0.12 m/s²

Part D:

Radius of flywheel = 0.600 m

Angular acceleration of flywheel (αₐ) = 0.200 rad/s²

Angular speed = ω = 0 m/s²

The tangential acceleration of a point after 60° turn (αₓ₁) = The tangential acceleration of a point at the start (αₓ)

= αₓ₁ = αₐ × r

= αₓ₁ = 0.200 × 0.600

= αₓ₁ =  0.12 m/s²

Part E:

Radius of flywheel = 0.600 m

Angular acceleration of flywheel (αₐ) = 0.200 rad/s²

Angular speed = ω = 0 m/s²

Angular speed after 60° turn = ω₁ = √(ω² + (2×α×θ))

To find θ,

= θ = 60Π / 180

= θ = Π/30

= θ = 1.04 rad

Thus, ω₁ = √(0 + 2 × 1.04 × 0.2)

= ω₁ = 0.644 rad/s

The radial acceleration of a point after 60° turn (αₓ₂) =

= αₓ₂ = r × ω₁²

= αₓ₂ = 0.600 × 0.644²

= αₓ₂ = 0.248 m/s²

Part F:

Radius of flywheel = 0.600 m

The tangential acceleration of a point after 60° turn (αₓ₁) = 0.12 m/s²

The radial acceleration of a point after 60° turn (αₓ₂) = 0.248 m/s²

The magnitude of resultant acceleration of a point on the rim after 60° turn (α₃) =

= α₃ = √ (αₓ₂² + αₓ₁²)

= α₃ = √ (0.12² + 0.248²)

= α₃ = 0.275 m/s²

Part G:

Radius of flywheel = 0.600 m

Angular acceleration of flywheel (αₐ) = 0.200 rad/s²

Angular speed = ω = 0 m/s²

The tangential acceleration of a point after 120° turn (αₓ₁) = The tangential acceleration of a point at the start (αₓ)

= αₓ₁ = αₐ × r

= αₓ₁ = 0.200 × 0.600

= αₓ₁ =  0.12 m/s²

Part H:

Radius of flywheel = 0.600 m

Angular acceleration of flywheel (αₐ) = 0.200 rad/s²

Angular speed = ω = 0 m/s²

Angular speed after 120° turn = ω₁ = √(ω² + (2×α×θ))

To find θ,

= θ = 120Π / 180

= θ = 2Π/3

= θ = 2.09 rad

Thus, ω₁ = √(0 + 2 × 2.09 × 0.2)

= ω₁ = 0.836 rad/s

The radial acceleration of a point after 120° turn (αₓ₂) =

= αₓ₂ = r × ω₁²

= αₓ₂ = 0.600 × 0.836²

= αₓ₂ = 0.502 m/s²

Part I:

Radius of flywheel = 0.600 m

The tangential acceleration of a point after 120° turn (αₓ₁) = 0.12 m/s²

The radial acceleration of a point after 120° turn (αₓ₂) = 0.502 m/s²

The magnitude of resultant acceleration of a point on the rim after 120° turn (α₃) =

= α₃ = √ (αₓ₂² + αₓ₁²)

= α₃ = √ (0.12² + 0.502²)

= α₃ = 0.515 m/s²

To know more about Radial, Tangential and Resultant Acceleration:

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