(20%) Problem 5: A yo-yo is made of two uniform disks, each of mass land radius

Question

(20%) Problem 5: A yo-yo is made of two uniform disks, each of mass land radius R, which are glued to a smaller central axle of negligible mass and radius 0.5R (see figure) A string is wrapped tightly around the axle. The yo-yo is then released from rest and allowed to drop downwards, as the string unwinds without slipping from the central axle. Side vievw R/2 Otheexpertta.com " ee 33% Part (a) Find the moment of inertia. I, ofthe yo-yo with respect to an axis through the common centers of the disks. in terms of the mass and radius @ 33% Part (b) Find the linear speed y of the vo-vo, after it has descended a distance H 33% Part (c) Calculate the magnitude of the linear velocity V, in meters per second, ofthe yo-yo after it has fallen a distance 0.49 m. - 2.19 Grade Summary 006 1006 Potential Submissions Attempts remaining:9 (00 per attempt) detailed view cotan asinacos0 atan acotansinhO coshtanhO cotanh0 006 END Degrees O Radians BACKSPAC CLEAR Submit Hint I give up Hints:-56 deduction per hint. Hints remaining: Feedback: 1% deduction per feedback.

Explanation / Answer

(a)

moment of inertia

I = M*R^2

(b)

torque on yo-yo = I * alpha

(0.5R * T) = M*R^2 *( a / 0.5R)

where T = tension in string

T = 4M*a

Fnet = m*a in vertical,

2M*g - T = 2M*a

2M*g - 4M*a = 2M*a

a = g / 3

a = 9.81 / 3 = 3.27 m/s^2

using equation of motion

v^2 - u^2 = 2*a*s

v^2 - 0 = 2*3.27*H

V = 2.56 * sqrt(H)

(c)

H = 0.43 m

v = 2.56 * sqrt(0.49)

v = 1.8 m/s

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