Physics Question on Force

Question

Hello, if someone may solve all this please with the steps on each problem that would be great. I'm having problems figuring this out. URGENT

Answer 1

1)

a) There are two forces:

T: as drawn

G: gravity due to the mass M of the pulley

b)

Moment of T is TR

Moment of G is 0, because the pulley center of gravity is also the center of rotation.

c)

TR = Iθ"

T = Iθ"/R = MR²θ"/2R = MRθ"/2

2)

a) There are two forces:

T' as drawn upward

G: force of gravity downward

b)

G - T' = ma

T' = G - ma

3)

T = T' by Newton's Third Law

MRθ"/2 = mg - ma

Ma/2 = mg - ma

a = mg/(M/2 + m)

Substituting actual values:

a = 1kg × 10m/s² / (3kg + 1kg) = 2.5m/s²