Question

A solid, horizontal cylinder of mass 18.0 kg and radius 1.70.0 m rotates with an angular speed of 40 rad/s about a fixed vertical axis through its center. A 0.8 kg piece of putty is dropped vertically onto the cylinder at a point 0.300 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system.

Answer 1

Answer:39.88 rad/s

Step-by-step explanation:

Given

mass of cylinder m_1=18 kg

radius R=1.7 m

angular speed
`\omega =40rad/s`

mass of
`m_2=0.8 kg` dropped at r=0.3 m from center

let
`\omega _2` be the final angular velocity of cylinder

Conserving Angular momentum

`L_1=L_2`

`\left ( (m_1R^2)/(2)\right )\omega =\left ( (m_1R^2)/(2)+m_2r^2\right )\omega _2`

`\left ( (18\cdot 1.7^2)/(2)\right )\cdot 40=\left ( (18\cdot 1.7^2)/(2)+0.8\cdot 0.3^2\right )\omega _2`

`26.01* 40=26.082* \omega _2`

`\omega _2=39.88 rad/s`