Problem — Which ω(t) for a braking disc

Problem

A rotating disc is subject to a constant friction torque that slows it down until it stops. Which of the $\omega(t)$ graphs describes its motion?

Solution

A constant friction torque produces, via $\tau = I\alpha$, a constant (and negative) angular acceleration. When $\alpha$ is constant, $\omega$ varies linearly with time: the graph is a decreasing straight line that brings $\omega$ to zero. $\omega(t) = \omega_0 - |\alpha|\,t$ Graph B (curved decay, typical of friction proportional to $\omega$) and graph C (constant) do not match. $\ev{\text{Graph A}}$

Connections

Topics: Dinamica rotazionale Concepts: Accelerazione angolare Skills: Lettura dei grafici Objects: Disco rotante