Question

Angular kinematics equation without final angular velocity

a) ω_f = ω_i + αt
b) ω_f = ω_i + τ/I
c) τ = Iα
d) ω_f = τ/I

Answer 1

The correct angular kinematics equation without the final angular velocity is ωf = ωi + αt (option a) , equivalent to its linear motion counterpart. This equation relates initial angular velocity (ωi), angular acceleration (α), and time (t). Another equation to find the final angular velocity using other known values is ωf² = ωi² + 2αθ.

Step-by-step explanation:

The question asks which angular kinematics equation doesn't include the final angular velocity (ωf), and the provided equations pertain to rotational motion in Physics. The correct angular kinematics equation that relates initial angular velocity (ωi), angular acceleration (α), and time (t) without reference to the final angular velocity is given by:

ωf = ωi + αt

This equation is analogous to the translational kinematics equation of linear motion, v = u + at, where ω corresponds to velocity (v), α to acceleration (a), and t to time (t). An angular kinematics equation that doesn't explicitly include ωf but relates to finding the final angular velocity using initial conditions and the angular acceleration is:

ωf² = ωi² + 2αθ

This indicates that ωf (final angular velocity) can be calculated if ωi (initial angular velocity), α (angular acceleration), and θ (angular displacement) are known. This is similar to the linear kinematics equation vf² = ui² + 2as.