Physics

Problem

![](https://storage.googleapis.com/diraq-contents/question-bank/question-images/13a1e0822c3a/2025_11_20_6dc4cc214b3dd4e3d6d5g-16.jpg) 2000 M 3 . A pulley of radius

R_{1}

and rotational inertia

I_{1}

is mounted on an axle with negligible friction. A light cord passing over the pulley has two blocks of mass

m

attached to either end, as shown above. Assume that the cord does not slip on the pulley. Determine the answers to parts a . and b . in terms of

m, R_{1}, I_{1}

, and fundamental constants. a. Determine the tension T in the cord. b. One block is now removed from the right and hung on the left. When the system is released from rest, the three blocks on the left accelerate downward with an acceleration

g / 3

. Determine the following. i. The tension

\mathrm{T}_{3}

in the section of cord supporting the three blocks on the left ii. The tension

\mathrm{T}_{1}

in the section of cord supporting the single block on the right iii. The rotational inertia

I_{1}

of the pulley ![](https://storage.googleapis.com/diraq-contents/question-bank/question-images/b4f67d2efc5c/2025_11_20_6dc4cc214b3dd4e3d6d5g-16.jpg) c. The blocks are now removed and the cord is tied into a loop, which is passed around the original pulley and a second pulley of radius

2 \mathrm{R}_{1}

and rotational inertia

16 \mathrm{I}_{1}

. The axis of the original pulley is attached to a motor that rotates it at angular speed

\omega_{1}

, which in turn causes the larger pulley to rotate. The loop does not slip on the pulleys. Determine the following in terms of

\mathrm{I}_{1}, \mathrm{R}_{\mathrm{I}}

, and

\omega_{1}

. i. The angular speed

\omega_{2}

of the larger pulley ii. The angular momentum

\mathrm{L}_{2}

of the larger pulley iii. The total kinetic energy of the system

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