A 6.00 kg mass is connected by a light cord to a 1.00 kg mass on a smooth surface as shown in the figure. The pulley rotates about a frictionless axle and has a moment of inertia of 0.400 k∙m2 and a radius of 0.700 m. Assuming that the cord does not slip on the pulley, find (a) the acceleration of the two masses

(b) the tension T1 (attached to the hanging mass).
(b) the tension T2

really confused on this problem. I'm not sure which equations to use?

To solve this problem, you can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F = ma).

Let's start by analyzing the motion of the two masses separately.

For the hanging mass (1.00 kg), the only force acting on it is the force of gravity (mg), where g is the acceleration due to gravity (approximately 9.8 m/s^2). Since the mass is accelerating downward, the net force acting on it is the tension force (T1) minus the force of gravity: T1 - mg.

For the 6.00 kg mass on the smooth surface, there are two forces acting on it: the tension force (T2) and the force of friction. Since the surface is smooth, there is no friction.

Now, let's solve the problem step by step:

(a) Acceleration of the two masses:

Since the pulley does not have any friction, the tensions on both sides of the pulley are equal (T1 = T2).

For the hanging mass:
T1 - mg = ma1

For the 6.00 kg mass:
T2 = m2a2

Since T1 = T2:
ma1 - mg = m2a2

Substituting the given masses:
(1.00 kg)a1 - (1.00 kg)(9.8 m/s^2) = (6.00 kg)a2

Simplifying the equation:
a1 - 9.8 m/s^2 = 6a2

(b) Tension T1 (attached to the hanging mass):

Using the derived equation from part (a):
T1 = ma1 + mg

Substituting the given values:
T1 = (1.00 kg)a1 + (1.00 kg)(9.8 m/s^2)

(b) Tension T2:

T2 = m2a2

Substituting the given values:
T2 = (6.00 kg)a2

Now you have two equations with two unknowns (a1 and a2). Solve these equations simultaneously to find the values of acceleration (a1 and a2), tension (T1), and tension (T2).

Note: To solve for a1 and a2, you can use algebraic methods such as substitution or elimination, or you can use graphical methods such as plotting the equations and finding their intersection point.