Question

If a rigid body has a constant angular acceleration, what is the functional form of the angular position?

a) θ = ωt
b) θ = ωt + 1/2 αt^2
c) θ = αt
d) θ = √αt

Answer 1

The functional form of the angular position when a rigid body has constant angular acceleration is θ = ω0t + ½αt2. Option b) is the correct answer to the student's question.

Step-by-step explanation:

If a rigid body has a constant angular acceleration, the functional form of the angular position is given by the kinematic equation analogous to the equation for linear motion with constant acceleration. The equation for the angular position (θ) as a function of time (t), initial angular velocity (ω0), and angular acceleration (α) is:

θ = ω0t + ½αt2

Using the provided options, the correct answer is b) θ = ωt + ½ αt2.

If the angular acceleration of a rigid body is zero, the functional form of the angular velocity is simply the constant angular velocity (ω) times time (t), which is θ = ωt. The equation defining angular velocity (ω) as a function of time is ω = ω0 + αt when α is constant.