Question

If a rigid body has a constant angular acceleration, what is the functional form of the angular velocity in terms of the time variable?

a) ω = αt
b) ω = α/t
c) ω = αt^2
d) ω = √αt

Answer 1

The functional form of angular velocity for a rigid body with a constant angular acceleration is ω = ω0 + αt; if initial angular velocity is zero, then it simplifies to ω = αt.

Step-by-step explanation:

If a rigid body has a constant angular acceleration, the functional form of the angular velocity in terms of the time variable can be described by the equation ω = ω0 + αt, where ω is the final angular velocity, ω0 is the initial angular velocity, α is the constant angular acceleration, and t is the time elapsed.

This equation is directly analogous to the equation for constant linear acceleration in linear kinematics, just with angular variables substituted in for their linear counterparts. Given the options provided, the correct functional form is a) ω = αt, assuming that the initial angular velocity (ω0) is zero.