How much wire do you pull out of this spool and how fast is it spinning?

Question

Wire is often delivered wrapped on a large cylindrical spool. Suppose such a spool is supported by resting on a horizontal metal rod that is pushed through a hole that runs through the center of the spool. A worker is pulling some wire off the spool by exerting a force on it something like is shown in the diagram at the right. (If you have ever bought wire in a hardware store, this is the way they usually store and dispense it.)

Suppose the spool rotates on the rod essentially without friction. The spool is approximately a uniform cylinder with a mass of 50 kg and a radius of 30 cm. The worker pulls on the wire for 2 seconds with a force of 30 N. At the end of the 2 seconds he immediately clamps on a brake which very quickly stops the spool's rotation. Just before he put the brake on, how fast was the spool rotating? How much wire did he pull off the spool?

Answer 1

This is turned into a straightforward constant-acceleration kinematics problem by finding the acceleration of the cylinder. The moment of inertia of a solid cylinder I = mr^2/2. Angular acceleration α = T/I where torque T = Fr. Ang. rate = αt. Total angle θ = αt^2/2 and total length unwound = θr.

Answer 2

Run your fishing line by using the 1st instruction manual on your rod. then you certainly're going to desire to open the bail, and someplace on the spool, merely tie 2 consecutive overhand knots. you like those knots to be tight. then you certainly merely snip off the surplus line coming from the knot. close your reels' bail. Then, you will desire to hold your appropriate hand (or your left hand in case you retrieve righty with spinning reels) some inches under the 1st instruction manual. This hand is going to make constructive that the line keeps to be tight on an analogous time as occurring the spool. If it would not go on the spool tight, your line would be loose and supply you extra "loops" and "birds nest". shop reeling till your spool is merely approximately comprehensive or comprehensive.