Consider a stainless steel annular disk with an outer radius68mm and inner radiu
ID: 2192957 • Letter: C
Question
Consider a stainless steel annular disk with an outer radius68mm and inner radius7.4mm. The mass of the disk is1349grams.
The stainless steel annular disk is allowed to rotate on a frictionless table with the rotation axis at its center. The disk has a small cylinder rigidly mounted at the top concentrically. The cylinder's radius is12.5mm, and the mass of the cylinder is negligible. A string is wrapped around the cylinder, and a hanging mass of19.3g is tied at the other end of the string. When the mass falls under gravity, it causes the stainless steel annular disk to rotate. Ignoring the string's mass, and assuming that the string's motion is frictionless.
How much distance has the hanging mass been falling by this time?
Explanation / Answer
Say you have a stainless steel annular disk with an outer radius 68 mm and inner radius 7.9 mm. The mass of the disk is 1346 grams. The disk is allowed to rotate on a frictionless table with the rotation axis at its center. The disk has a small cylinder rigidly mounted at the top concentrically. The cylinder's radius is 12.8 mm, and the mass of the cylinder is negligible. A string is wrapped around the cylinder, and a hanging mass of 19.3 g is tied at the other end of the string. When the mass falls under gravity, it causes the stainless steel annular disk to rotate. Ignoring the string's mass, and assuming that the string's motion is frictionless, what is the angular acceleration of the stainless steel annular disk? I found the moment of inertia of the disk to be .003154 kg*m^2 using I = m/2(R1^2 + R2^2), which was correct. I know that angular acceleration = change in angular velocity/change in time and that angular acceleration = a/r but I'm not sure how to use these equations to find an answer. You need to calculate the torque. T = force*radius of the cylinder Then the angular analogy to Newton's 2nd (F=ma) is T = I*alpha where I is the moment of inertia and alpha is the angular acceleration.