Question

A ring and a disc, both with radius r and mass M, roll down an incline. Find their angular and linear accelerations.

Answer 1

Step-by-step explanation:

Given

both ring and disc have mass m and radius r

Let
`\theta`be the inclination of plane with horizontal

`f_r` be the friction force which provides torque to object

`mgsin\theta -f_r=ma`

and
`I\alpha =f_r* r` ---1

where I=moment of inertia

`mgsin\theta -(I\aplha )/(r)=ma`

and we know for pure rolling a=\alpha \times r[/tex]

thus

`a=(gsin\theta )/(1+(I)/(mr^2))`

Thus Linear acceleration of ring with
`I=mr^2`

`a=(gsin\theta )/(2)`

For disc
`I=(mr^2)/(2)`

`a=(2gsin\theta )/(3)`

Angular acceleration for ring

`\alpha =(gsin\theta )/(2r)`

For disc

`\alpha =(2gsin\theta )/(3r)`