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Question

# A wheel with radius 30 cm is rotating at a rate of 10 rev/s. At t = 10 s the angular speed begins to increase at a rate of 1.4 rad/s/s. At t = 15 s, what is the angular speed in radians per second?

Solution

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$\underline{\text{Identify the unknown:}}$

The final angular speed

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

From part (a), initial angular speed: $\omega_i= 62.83 \;\mathrm{rad/s}$

Angular acceleration: $\alpha= 1.4 \;\mathrm{rad/s^2}$

Time interval: $\Delta t= 15 - 10 = 5 \;\mathrm{s}$

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

The angular acceleration:

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

$\omega_f = \omega_i + (\alpha \Delta t)$

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

$\omega_f = 62.83 + (1.4 \times 5) = \boxed{69.83 \;\mathrm{rad/s}}$

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