Question

Asked Dec 19, 2019

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An oversized yo-yo is made from two identical solid disks

each of mass M= 2.00 kg and radius R = 10.0 cm. The two

disks are joined by a solid cylinder of radius r = 4.00 cm and

mass m = 1.00 kg as in Figure P8.40. Take the center of the

cylinder as the axis of the system, with positive torques directed

to the left along this axis. All torques and angular variables

are to be calculated around this axis. Light string is wrapped

around the cylinder, and the system is then allowed to drop

from rest. (a) What is the moment of inertia of the system?

Give a symbolic answer. (b) What torque does gravity exert on

the system with respect to the given axis? (c) Take downward as

the negative coordinate direction. As depicted in Figure P8.40,

is the torque exerted by the tension positive or negative? Is

the angular acceleration positive or negative? What about the

translational acceleration? (d) Write an equation for the angular

acceleration ∝ in terms of the translational acceleration ∝ in terms of the translational acceleration a and radius r. (Watch the sign!) (e) Write Newton’s second lawfor the system in terms of m, M, a, T, and g. (f) Write Newton’s second law for rotation in terms of I, ∝, T, and r. (g) Eliminate

∝ from the rotational second law with the expression found in

part (d) and find a symbolic expression for the acceleration a

in terms of m, M, g, r, and R. (h) What is the numeric value for

the system’s acceleration? (i) What is the tension in the string?

( j) How long does it take the system to drop 1.00 m from rest?

Step 1

(a). the moment of inertia of the disc and cylinder is

Step 2

So the moment of inertial of the system is

Step 3

(b). the gravitational force that passes through the rotational axis has no lever arm in it with r...

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