#### Question

A rotating wheel accelerates at a constant rate from an angular speed of 24 rad/s to 36 rad/s in a time interval of 3 s. What is the angular acceleration in rad/s/s?

#### Solution

Verified#### Step 1

1 of 2$\underline{\text{Identify the unknown:}}$

The angular acceleration

$\underline{\text{List the Knowns:}}$

Initial angular speed: $\omega_i= 24 \;\mathrm{rad/s}$

Final angular speed: $\omega_f= 36 \;\mathrm{rad/s}$

Time interval: $\Delta t= 3 \;\mathrm{s}$

$\underline{\text{Set Up the Problem:}}$

The angular acceleration:

$\alpha = \dfrac{\Delta \omega}{\Delta t} = \dfrac{\omega_f - \omega_i}{\Delta t}$

$\underline{\text{Solve the Problem:}}$

$\alpha = \dfrac{36 - 24}{3} = \boxed{4 \;\mathrm{rad/s^2}}$

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