Two metal disks, one with radius R and the other with radius 2R, are welded toge

Question

Two metal disks, one with radius R and the other with radius 2R, are welded together and mounted on a frictionless axis through their common center. A light string is wrapped around the edge of the smaller disk and a block of mass M is suspended from the free end of the string. The moment of inertia of the pulley is I (a) (20 points) Calculate the acceleration of the mass M (b) (5 points) Same question, but assume that the rope is Note: A similar figure has appeared on several of my old final wrapped around the larger disk. exams. This is not the same problem. Read the problenm. 2R MacBook Air

Explanation / Answer

Let acceleration be a and tension be T,

writing force equation on block,

Mg - T = Ma

now writing torque equation on pully:

TR = i alpha where alpha = a/R

T = i a/R^2

adding the force equation to it,

Mg = (M+i/R^2)a

a = Mg/(M+i/R^2) answer

b] writing force equation on block,

Mg - T = Ma

now writing torque equation on pully:

T*2R = i alpha where alpha = a/2R

T = i a/(4R^2)

adding the force equation to it,

Mg = (M+i/(4R^2))a

a = Mg/(M+i/(4R^2)) answer

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.