Physics

Physics

Problem

A student graphs the angular position θ\theta (in radians) of a rotating wheel as a function of time tt (in seconds). The graph is a straight line with positive slope. Which physical quantity does the slope of the θ\theta–tt graph most directly represent? a) the wheel’s angular acceleration b) the wheel’s angular velocity c) the tangential speed of a point on the rim d) the wheel’s rotational frequency (revolutions per second)
Intuitive explanation

The slope of a θ\theta–tt graph tells you how much the angle changes per unit time—that's the definition of angular velocity ω\omega. Since the graph is a straight line, the slope is constant, meaning the wheel rotates at a steady rate with no angular acceleration. Reading the slope directly from the graph gives you ω\omega in rad/s.

Intuitive explanation

The slope of a θ\theta–tt graph tells you how much the angle changes per unit time—that's the definition of angular velocity ω\omega. Since the graph is a straight line, the slope is constant, meaning the wheel rotates at a steady rate with no angular acceleration. Reading the slope directly from the graph gives you ω\omega in rad/s.

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