At a given instant the rolling cylinder C in the accompanyin

At a given instant, the rolling cylinder C in the accompanying diagram has omega_C = 2 rad/s and alpha_C = 1.5 rad/s^2. Find the velocity and acceleration of points N and E.

Solution

angular acceleration and angular acceleration will be same for all the 4 points- E W N S.

But the values of velocity and acceleration will be different since the centre of rotation is point S and point E, N and W are at unequal distances from the center of rotation.

SE = SW = 0.3 x root(2) = 0.4243 m

and SN = 2 x 0.3 = 0.6 m

So, velocity of point W = velocity of point E = 0.4243 x 2 = 0.8486 m/sec

Acceleration of point W =Acceleration of point E = 0.4243 x 1.5 = 0.63645 m/sec2

Now, Velocity of point N = 0.6 x 2 = 1.2 m/sec

Acceleration of point N = 0.6 x 1.5 = 0.9 m/sec2