In the figure, Pulley A, rotating at 20 rad/s, controls the motion of Pulley B. The motor of pulley A is cut off, and friction eventually brings the pulleys to a stop with an angular acceleration of α = -2.5t rad/s2. If there is no slippage, determine:a. The angular velocity of B with respect to time b. The angular displacement of B during thedecelerationc. The acceleration of point C with respect to time The image illustrates a mechanical pulley system composed of two pulleys, labeled A and B, connected by a belt or rope labeled C. ### Description of Components:- **Pulley B**: - A larger pulley with a radius of 6 inches. - Mounted on a fixed axis. - Appears to rotate clockwise.- **Pulley A**: - A smaller pulley with a radius of 3 inches. - Also mounted on a fixed axis. - Marked with angular velocity (\(\omega_A\)) and angular acceleration (\(\alpha_A\)) indicating its rotational motion.- **Belt/Rope (C)**: - Connects pulleys A and B. - Transfers rotational motion from one pulley to the other.### Explanation:The diagram demonstrates the mechanics of a pulley system where rotational motion is transferred between two pulleys of different sizes through a connecting belt. The larger pulley B is twice the radius of the smaller pulley A, which would affect the rotational velocity and torque transmitted between them. This setup is commonly used in mechanical applications to either increase force or change the direction of motion.

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Answered: Pulley A, rotating at 20 rad/s,…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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In the figure, Pulley A, rotating at 20 rad/s, controls the motion of Pulley B. The motor of pulley A is cut off, and friction eventually brings the pulleys to a stop with an angular acceleration of α = -2.5t rad/s2. If there is no slippage, determine: a. The angular velocity of B with respect to time b. The angular displacement of B during the deceleration c. The acceleration of point C with respect to time

The image illustrates a mechanical pulley system composed of two pulleys, labeled A and B, connected by a belt or rope labeled C.

### Description of Components:

- **Pulley B**:
- A larger pulley with a radius of 6 inches.
- Mounted on a fixed axis.
- Appears to rotate clockwise.

- **Pulley A**:
- A smaller pulley with a radius of 3 inches.
- Also mounted on a fixed axis.
- Marked with angular velocity (\(\omega_A\)) and angular acceleration (\(\alpha_A\)) indicating its rotational motion.

- **Belt/Rope (C)**:
- Connects pulleys A and B.
- Transfers rotational motion from one pulley to the other.

### Explanation:

The diagram demonstrates the mechanics of a pulley system where rotational motion is transferred between two pulleys of different sizes through a connecting belt. The larger pulley B is twice the radius of the smaller pulley A, which would affect the rotational velocity and torque transmitted between them. This setup is commonly used in mechanical applications to either increase force or change the direction of motion.

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