Question

A heavy plank is moving with horizontal acceleration $a=2m/s^2$. A hollow cylinder of mass $m=3kg$ and $radius=25cm$ is on the upper surface of the plank and moves without slipping. Find the angular acceleration (about the axis in $rad/s^2$) of the hollow cylinder?

Answer 1

Problem will be very easily solved if we go in the frame of plank.

In the frame of plank pseudo force of $ma$ will be acting on it.

Let friction force be $f$ and acceleration of cylinder in frame of plank be $a_1$

We can write the following three equations:

• $ma-f=m{a}_1$
  
• $fr=m{r}^2\alpha$
  
• $a_1=\alpha \times r$
  

$f=3$ $a_1=1$

angular acceleration $\alpha =\frac{a_1}{r}$=$4$