When a solid object rotates with a constant angular acceleration, which of the following is true?

Question

BlackTom AI · Accepted Answer

To analyze the statement, let's first recall the relation between torque, moment of inertia, and angular acceleration for a rigid body rotating about a fixed axis: τ = I α, where I is the moment of inertia about the rotation axis and α is the angular acceleration.
Option 1: 'The net torque applied to the object must be non-zero constant.' If the angular acceleration α is constant and nonzero, then τ = I α is a constant value (assuming I is constant, which it is for a rigid solid about a fixed axis). Hence the net torque must be a nonzero constant. This aligns with the given condition of constant angular acceleration.
Option 2: 'The net torque applied to the object must be zero.' This would imply α = 0 (no angular acceleration) if I is finite, which contradicts the premise of constant angular acceleration. Therefore, this statement is incorrect.
Option 3: 'All points rotate with the same centripetal acceleration.' In a rigid body undergoing rotation, the centripetal (radial) acceleration a_c = ω^2 r depends on the distance r from the rotation axis. Points farther from the axis experience larger a_c, so not all points share the same centripetal acceleration. This makes the statement false.
Option 4: 'The net torque applied to the object must increase.' If α is constant, the torque τ = I α remains constant (assuming I does not change). Therefore, the torque need not increase over time; it stays the same. This statement is incorrect.

SPHY001 Practice Quiz - Unit 10 | LA050

When a solid object rotates with a constant angular acceleration, which of the following is true?

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