This is a rotational kinematics problem because of the rotational velocity, time, and #of revolutions.

Rotational kinematic equations:

$\overline{){{\mathbf{\omega}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{\alpha}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{\theta}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{(}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{+}}{{\mathbf{\omega}}}_{{\mathbf{f}}}{\mathbf{)}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{\theta}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{t}}{\mathbf{}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\alpha}}{{\mathbf{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{{\mathbf{\omega}}}_{{\mathbf{f}}}^{{\mathbf{2}}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{2}}{\mathbf{\alpha}}{\mathbf{\u2206}}{\mathbf{\theta}}}$

We are given several variables disguised in the long narration. Let's list down the variables so that we make sense of this scenario involving rotational kinematics.

- ω
_{0}= 500 rev/min(2π rad/1rev)(1min/60s) = 52.36 rad/s - ω
_{f}= ? - t = 31.0s
- Δθ = 170 rev(2πrad/1rev) = 1068 rad
- α = ?

A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 41.0 kg and diameter 76.0 cm . The power is off for 31.0 s and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 170 complete revolutions.

You may want to review (Pages 278 - 280).

For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Rotation with constant angular acceleretion.

(a) At what rate is the flywheel spinning when the power comes back on?

ω = ____ rad/s

(b) How long after the beginning of the power failure would it have taken the flywheel to stop if the power had not come back on?

(c) How many revolutions would the wheel have made during this time?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Equations of Rotational Motion concept. You can view video lessons to learn Equations of Rotational Motion. Or if you need more Equations of Rotational Motion practice, you can also practice Equations of Rotational Motion practice problems.

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Based on our data, we think this problem is relevant for Professor Meyer's class at UGA.