Which graph best describes the angular position of a wheel with positive constant angular acceleration over time?

Master StraighterLine Physics Test. Study with diverse questions and detailed answers. Excel in your physics course!

Multiple Choice

Which graph best describes the angular position of a wheel with positive constant angular acceleration over time?

The graph that best represents the angular position of a wheel with positive constant angular acceleration over time is a parabola that opens upwards. This is because when an object is undergoing constant angular acceleration, the angular position does not change linearly; instead, it follows a quadratic relationship with time. Mathematically, angular position (θ) as a function of time (t) under constant angular acceleration (α) can be expressed by the equation: \[ \theta(t) = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 \] where \( \theta_0 \) is the initial angular position, \( \omega_0 \) is the initial angular velocity, and \( \alpha \) is the constant angular acceleration. The term \( \frac{1}{2} \alpha t^2 \) indicates that the angular position increases more rapidly over time, resulting in a curve that shows a parabolic shape opening upwards. This shape reflects the increasing displacement covered by the wheel due to the constant acceleration, which leads to a larger change in angular position as time progresses. In contrast, a straight line would suggest a constant angular velocity (not acceleration), a sine wave would

The graph that best represents the angular position of a wheel with positive constant angular acceleration over time is a parabola that opens upwards. This is because when an object is undergoing constant angular acceleration, the angular position does not change linearly; instead, it follows a quadratic relationship with time.

Mathematically, angular position (θ) as a function of time (t) under constant angular acceleration (α) can be expressed by the equation:

[

\theta(t) = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2

]

where ( \theta_0 ) is the initial angular position, ( \omega_0 ) is the initial angular velocity, and ( \alpha ) is the constant angular acceleration. The term ( \frac{1}{2} \alpha t^2 ) indicates that the angular position increases more rapidly over time, resulting in a curve that shows a parabolic shape opening upwards. This shape reflects the increasing displacement covered by the wheel due to the constant acceleration, which leads to a larger change in angular position as time progresses.

In contrast, a straight line would suggest a constant angular velocity (not acceleration), a sine wave would

More practice questions