A string is wrapped around a pulley of radius .20m and momentum of inertia .40 kg•m^2. The string is pulled with a force of 28 N. what is the magnitude of the resulting angular acceleration?

Can someone please go through the steps or at least guide me through them. I missed a few days in class and am trying to figure this out without any notes on it or anything.

whatis missing on what I just did?

Sorry it posted twice on accident

To determine the magnitude of the resulting angular acceleration, you can use the formula for torque. The torque acting on an object is equal to the product of the force applied and the distance from the point of rotation.

Step 1: Calculate the torque (τ).

The formula for torque (τ) is given by:

τ = r * F

Where:
τ = torque
r = radius of the pulley (0.20m)
F = applied force (28 N)

Substituting the known values into the formula:

τ = 0.20m * 28 N
= 5.6 N·m

Step 2: Calculate the angular acceleration (α).

The formula for torque (τ) is also given by:

τ = I * α

Where:
I = moment of inertia (0.40 kg·m²)
α = angular acceleration

Substituting the known values into the formula:

5.6 N·m = 0.40 kg·m² * α

Solving for α:

α = 5.6 N·m / 0.40 kg·m²
= 14 rad/s²

Therefore, the magnitude of the resulting angular acceleration is 14 rad/s².

To find the magnitude of the resulting angular acceleration, we can use Newton's second law for rotational motion, which states that the net torque acting on an object is equal to the moment of inertia of the object multiplied by its angular acceleration.

The net torque acting on the pulley can be determined by considering the force applied and the radius of the pulley. The torque is given by the equation:

τ = r * F

where τ is the torque, r is the radius of the pulley, and F is the force applied.

In this case, the radius of the pulley is 0.20m and the force applied is 28N. Plugging in the values, we get:

τ = 0.20m * 28N

Next, we need to find the moment of inertia of the pulley. The moment of inertia is a measure of an object's resistance to changes in its rotational motion and depends on the distribution of mass in the object. For a solid cylinder like a pulley, the moment of inertia is given by:

I = 0.5 * m * r^2

where I is the moment of inertia, m is the mass of the pulley, and r is its radius.

The problem statement provides the moment of inertia of the pulley as 0.40 kg·m^2. However, we can calculate it using the formula above using the radius of the pulley. If you have the mass of the pulley, you can use the formula to calculate it and substitute the value into the equation.

Once you have the torque and moment of inertia, you can use Newton's second law for rotational motion to find the angular acceleration:

τ = I * α

where α is the angular acceleration.

Substituting the known values, we get:

0.20m * 28N = 0.40 kg·m^2 * α

Now you can solve for the angular acceleration, α, by rearranging the equation:

α = (0.20m * 28N) / 0.40 kg·m^2

Simplifying the expression:

α = 5.6 N·m / 0.40 kg·m^2

Finally, divide the units to obtain the magnitude of the resulting angular acceleration:

α = 14 N / 0.40 kg

α = 35 N/kg·m

Therefore, the magnitude of the resulting angular acceleration is 35 N/kg·m.