Question

A 1.6 kg bicycle wheel with a radius of 0.31 m turns at a constant angular speed of 27 rad/s when a(n) 0.33 kg reflector is at a distance of 0.19 m from the axle. What is the angular speed of the wheel when the reflector slides to a distance of 0.26 m from the axle? Answer in units of rad/s.

Answer 1

The guy above me is wrong because he treats the wheel as a disk, but is actually a ring, so the moment of inertia for the wheel should be (MR^2) instead of (1/2)(MR^2)

Step-by-step explanation:

I tried what he did and I got marked wrong, then use the ring formula and I got it right :)

Answer 2

angular speed = 25.393 rad/s

Step-by-step explanation:

Given Data:

weight of bicycle wheel is 1.6 kg

radius of bicycle wheel is 0.31 m

angular speed is 27 rad/s

weight of reflector uis 0.33 kg

reflector distance from axle is 0.19 m

we know that moment of inertia between two mass is calculated as

Moment of inertia
`I1 = (1)/(2) { MR^2 +m r^2 }`

`= (1)/(2)[ {1.6*0.31^2 + 0.33* 0.19^2}]`

= 0.0828

Moment of inertia I2

`= (1)/(2)[ {1.6*0.31^2 + 0.33* 0.26^2}]`

= 0.088

`(I1)/(I2) = 0.9405`

`\omega =  {(I1)/(I2) \omega _1`

`= 0.9405 * 27`

= 25.393 rad/s