Answer: a) 24.2 rad/s² b) 6.95 rad/s
Explanation:
So the cylinder's moment of inertia is , where M is the mass of the cylinder and R is its radius.
The problem you have here is that the axle is modifying it, so we use the parallel axis theorem:
Therefore
where D is the distance from the center of mass to the axis which is a radius R
Next the Momentum with respect to the center of mass of the cylinder is
because there are no other forces rather than the cylinder's weight, now kg*m^2
a ) replace and find
b) we start by assuming that the energy is conserved because the cylinder is rolling without sliding:
so the potential energy is given by
now you have that the same amount is going to be equal to the kinetic rotational energy of the cylinder so