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

Answer:

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 $I\alpha =f_r\times r$ ---1

where I=moment of inertia

$mgsin\theta -\frac{I\aplha }{r}=ma$

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

thus

$a=\frac{gsin\theta }{1+\frac{I}{mr^2}}$

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

$a=\frac{gsin\theta }{2}$

For disc $I=\frac{mr^2}{2}$

$a=\frac{2gsin\theta }{3}$

Angular acceleration for ring

$\alpha =\frac{gsin\theta }{2r}$

For disc

$\alpha =\frac{2gsin\theta }{3r}$