a uniform cylinder of mass m and radius r rolls on a fixed cylindrical surface of radius R. at a certain instant, the line OC has an angular velocity omega and angular accelaration alpha. find

1] the accelaration of point of contact p of the cylinder with respectto the surface

b] the kinetic energy of cyliner

note : O is the centre of cylindrical surface and C is the centre of uniform cylinder of mass m

a=a0−Rα ........i
Which yields a0=Rα+a
the equation of motion are
ΣFx=f=(M)a0
Στ=−f×R=(1/2MR^2)α..........iii
Negative sign shows that the torque of friction is opposite to the assume α.
From eqn i and ii we get
f=M(Rα)..........iv
Sunstituting the expression for f in eqn ii we obtain
Rα=−2/3a
From eqn i a0=−2/3+=1/3a
The maximum value of frictional force fmax=μN where N=Mg, from eqn ii
0.40N=M(1/3a)
=0.0Mg=M(1/3a)
a=(0.40)(3g)=1/2m/s^2
Which is the maximum acceleration the platform may have without slipping between the cylinder and the platform.