# A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The...

## Question:

A high-speed flywheel in a motor is spinning at {eq}500 \ rpm {/eq} when a power failure suddenly occurs. The flywheel has mass {eq}44.0 \ kg {/eq} and diameter {eq}75.0 \ cm {/eq}. The power is off for {eq}28.0 \ s {/eq} and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes {eq}170 {/eq} complete revolutions.

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

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?

## Rotational motion

We have to use the concept and equation of the rotational motion to find the solution to this problem. We have to use the rotational kinematics equation to establish the relation between the angular displacement, time and angular velocity

## Answer and Explanation:

**Given**

Initial angular speed {eq}\displaystyle w_{1} = \frac{2\pi*500}{60} = 52.36 \ rad/s {/eq}

Mass of the flywheel (m) = 44 kg

Radius of the flywheel (r) = 37.5 cm

time for power being off (t) = 28 s

Revolutions make by the flywheel {eq}\displaystyle \theta = 2\pi*170 = 1068.141 \ rad {/eq}

**(a)**

{eq}\displaystyle \theta = w_{1}t + 0.5\alpha*t^{2} \\ 1068.141 = (52.36*28) +(0.5*\alpha*28^{2}) \\ \alpha = -1.015 \ rad/s^{2} {/eq}

Now using the first kinematic equation

{eq}\displaystyle w_{2} = w_{1} + \alpha*t \\ w_{2} = 52.36 + (-1.015)*28 \\ w_{2} = 23.94 \ rad/s {/eq}

**(b)**

If the power had not come back, then final speed would be zero, therefore

{eq}\displaystyle w_{2} = w_{1} + \alpha*t \\ 0 = 52.36 + (-1.015)*t \\ t = 51.59 \ s {/eq}

**(c)**

Using the kinematic equation

{eq}\displaystyle w_{2}^{2} = w_{1}^{2} + 2\alpha\theta \\ 0 = 52.36^{2} + 2(-1.015)*\theta \\ \theta = 1350.527 \ rad {/eq}

#### Learn more about this topic:

from Physics 101: Help and Review

Chapter 17 / Lesson 15