Question

The angular velocity (ω) of a particle depends on its angular position (θ, measured with respect to a certain line of reference) by the rule ω = 2√θ. Find the angular acceleration α as a function of θ.

Answer 1

α = θ^(-1/2)

Step-by-step explanation:

The angular acceleration α is the derivative of angular velocity ω with respect to time, and it can be found by taking the derivative of ω with respect to θ.

Given: ω = 2√θ

To find α, we differentiate ω with respect to θ:

α = dω/dθ

Using the power rule of differentiation, we can differentiate 2√θ with respect to θ:

α = d/dθ (2√θ)

Using the chain rule, we can differentiate 2√θ with respect to θ:

α = 2 * (1/2) * θ^(-1/2) * dθ/dθ

Simplifying, we get:

α = θ^(-1/2)

So, the angular acceleration α as a function of θ is given by α = θ^(-1/2).