Question

A pulley which can rotate about an axis through its center consists of an
inner cylinder of radius R1 = 10 cm and an outer cylinder of radius R2 =
15 cm. Ropes wrapped around the cylinders are used to apply forces F1 =
16 N and F2 = 8 N as shown. The rotational inertia of the pulley is 0.025
kg∙m2. What is the magnitude of the angular acceleration of the wheel

Answer 1

I know angular acceleration\[\alpha=torque \div inertia\]

Answer 2

From Euler's Equations of motion, \[\sum \tau = I \alpha\]\[16 \cdot 0.1 + 8 \cdot 0.15 = 0.025 \alpha\]Assuming both forces act on the same side of the pulley system.

Answer 3

the answer is 16 rad/s\[^{2}\]

Answer 4

the forces act at a 90 degree angle. F1 is to the left, F2 is pointing down

Answer 5

Does it look like this?

Answer 6

F1 is also attached to the smaller radius