Question

Assignment Status Click here for detailed view Problem Status Completed Completed Completed Completed Partial (11%) Problem 5: A yo-yo is made of two uniform disks, each of mass Mand radius R. which are ued to a smaller central axle of ne ble mass and ra uS 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 Side view slipping from the central axle. R/2 Otheexpertta.com 33% Part (a) Find the moment of inertia, 1. of the 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 Vof the yo-yo, after it has descended a distance H. A 33% Part (c) Calculate the magnitude of the linear velocity in eters per second. of the yo-yo after it has fallen a distance 0.43 m. Grade Summary Deductions 100% Potential sino cos0 tano 7 8 9 HoME Sub Attempts remaining: 3 acoso asin() per attempt atano acotan sinho detailed view cosho tanh0 cotanh IVO BAC SPACE CLEAR Degrees O Radians Submit Hint Feedback I give up! Hints: Feedback 5% ded per feedback deduction per hint. Hints remaining:

Answer 1

(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(0.43)

v = 1.67 m/s

answer