A torque τ is applied to a rigid body with a moment of inertia I. If the torque is doubled, what happens to the angular acceleration? (2019)

1 question

1 item

Q: A torque τ is applied to a rigid body with a moment of inertia I. If the torque is doubled, what happens to the angular acceleration? (2019)

Solution: According to Newton's second law for rotation, τ = Iα. If τ is doubled, α also doubles.

Steps: 9

Step 1: Understand that torque (τ) is a force that causes rotation.
Step 2: Know that moment of inertia (I) is a measure of how difficult it is to change the rotation of an object.
Step 3: Recall Newton's second law for rotation, which states that torque (τ) equals moment of inertia (I) times angular acceleration (α): τ = Iα.
Step 4: If the torque (τ) is doubled, write it as 2τ.
Step 5: Substitute 2τ into the equation: 2τ = Iα'. Here, α' is the new angular acceleration.
Step 6: Since τ = Iα, we can replace τ in the new equation: 2(Iα) = Iα'.
Step 7: Simplify the equation: 2Iα = Iα'.
Step 8: Divide both sides by I (assuming I is not zero): 2α = α'.
Step 9: This shows that the new angular acceleration (α') is double the original angular acceleration (α).