If the moment of inertia of a body is increased, what happens to its angular acceleration for a constant torque?

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Q: If the moment of inertia of a body is increased, what happens to its angular acceleration for a constant torque?

Solution: According to Newton's second law for rotation, τ = Iα, if I increases and τ is constant, α must decrease.

Steps: 5

Step 1: Understand what torque (τ) means. Torque is a measure of how much a force acting on an object causes that object to rotate.
Step 2: Know that moment of inertia (I) is a property of an object that determines how difficult it is to change its rotation. A larger moment of inertia means it's harder to rotate the object.
Step 3: Remember 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 moment of inertia (I) increases while the torque (τ) remains constant, we can rearrange the equation to find angular acceleration (α): α = τ / I.
Step 5: Since τ is constant and I is increasing, the value of α (angular acceleration) must decrease because you are dividing a constant number by a larger number.