Physics

Physics

Problem

A disk spins counterclockwise and then experiences a constant clockwise angular acceleration until it stops. If counterclockwise is defined as the positive direction, which of the following correctly gives the signs of the initial angular velocity ωi\omega_i and the angular acceleration α\alpha during the slowing process? a) ωi\omega_i positive, α\alpha positive b) ωi\omega_i positive, α\alpha negative c) ωi\omega_i negative, α\alpha positive d) ωi\omega_i negative, α\alpha negative
Intuitive explanation

The key is recognizing that sign convention matters: counterclockwise is positive, so clockwise is negative. Since the disk starts spinning counterclockwise, ωi\omega_i is positive. The angular acceleration opposes the motion (it's slowing the disk down), so it points clockwise—opposite to the velocity direction. When acceleration opposes velocity, they have opposite signs, which is exactly what happens when an object decelerates.

Intuitive explanation

The key is recognizing that sign convention matters: counterclockwise is positive, so clockwise is negative. Since the disk starts spinning counterclockwise, ωi\omega_i is positive. The angular acceleration opposes the motion (it's slowing the disk down), so it points clockwise—opposite to the velocity direction. When acceleration opposes velocity, they have opposite signs, which is exactly what happens when an object decelerates.

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