(b) write an expression for the net external torque acting on the system of the two blocks + wheel + string about the wheel's axle. what are its rotation sense and vector direction? [note: the string is part of the system, so the string tension forces provide internal torques, not external torques.]

τext =(M*R*g)*(m₂ - m₁) / (m₁ + m₂)

The wheel is rotating clockwise. Its vector direction is - k  which is perpendicular to the plane of the wheel.

Explanation:

Given info

m₁ = mass of block 1

m₂ = mass of block 2

m₁ < m₂

M = Mass of the wheel

R = Radius of the wheel

I = Moment of inertia of the wheel = M*R²

We assume that the wheel is rotating clockwise since m₁ < m₂

In order to get an expression for the net external torque acting on the system we can apply the following equation

τext = I*α

where α is the angular acceleration of the wheel which can be found as follows

at = R*α   ⇒    α = at / R

then we have to compute the acceleration of the system (at), using the Newton's 2nd Law

Block 1:

∑Fy = m₁*at  (↑+)  ⇒    T - m₁*g = m₁*at    (I)

Block 2:

∑Fy = m₂*at  (↓+)  ⇒    - T + m₂*g = m₂*at    (II)

If  we apply  

(I) + (II)  ⇒        at = g*(m₂ - m₁) / (m₁ + m₂)

Now, we get α:

α = at / R = (g*(m₂ - m₁) / (m₁ + m₂)) / R

⇒     α = (g / R)*(m₂ - m₁) / (m₁ + m₂)

Finally

τext = I*α = (M*R²)*((g / R)*(m₂ - m₁) / (m₁ + m₂))

⇒   τext =(M*R*g)*(m₂ - m₁) / (m₁ + m₂)

The wheel is rotating clockwise. Its vector direction is - k  which is perpendicular to the plane of the wheel.

answer: the direction of the wind is expressed as the direction from which the wind is blowing. for example, easterly winds blow from east to west, while westerly winds blow from west to east.

explanation:

b. lifting dumbbell weight at 20-degree angle from the body after a 45-degree angle