Question

A spin bike has a flywheel in two parts—a 12.5 kg disk with radius 0.23 m, and a 7.0 kg ring with mass concentrated at the outer edge of the disk. A friction pad exerts a force of 9.7 N on the outside of the disk. A cyclist is pedaling, spinning the disk at a typical 180 rpm. If she stops pedaling, how long will it take for the flywheel to come to a stop?

Answer 1

To determine how long it takes for the flywheel to come to a stop, calculate the angular acceleration using the torque and moment of inertia. Then, use the angular acceleration to find the time.

Step-by-step explanation:

To determine how long it takes for the flywheel to come to a stop, we need to calculate the angular acceleration first. To do this, we can use the formula:

α = τ / I

Where α is the angular acceleration, τ is the torque, and I is the moment of inertia. The torque can be calculated using the formula:

τ = rF

Where r is the radius of the flywheel and F is the force exerted on it. Once we have the angular acceleration, we can use it to find the time it takes for the flywheel to come to a stop using the formula:

t = ω / α

Where t is the time, ω is the initial angular velocity, and α is the angular acceleration.

Answer 2

Step-by-step explanation:

Given

mass of disk
`m=12.5 kg`

radius of disc
`R=0.23 m`

mass of ring
`m_r=7 kg`

Force
`F=9.7 N`

`N=180 rpm`

`\omega =(2\pi N)/(60)`

`\omega =6\pi rad/s`

Total moment of inertia

=Moment of inertia of Disc +Moment of Inertia of ring

`=0.5\cdot 12.5* 0.23^2+7* 0.23^2`

`=13.25* 0.23^2=0.7009 kg-m^2`

Now Torque is
`T=F* R=I\cdot \alpha`

`9.7* 0.23=0.7* \alpha`

`\alpha =3.18 rad/s^2`

Now using
`\omega _f=\omega +\alpha t`

`\omega _f=0` here

`0=6\pi -3.18* t`

`t=(6\pi )/(3.18)`

`t=5.92 s`