**Problem 8: Another Gear**Two disks are connected to one another with a belt as shown. Both disks have mass \( m \) but the larger one has radius \( 4R \) and the smaller has radius \( R \). The larger disk is powered by a motor that produces a constant torque, \( \tau_0 \), in the counterclockwise direction.(a) By using the rotational equivalent of Newton’s laws on the larger disk, show that the difference in the tension at the top with the tension at the bottom is:\[ T_{\text{top}} - T_{\text{bot}} = \frac{1}{4R} (\tau_0 - 2mRa), \]where \( a \) is the linear acceleration of the belt. (b) Do the same (find \( T_{\text{top}} - T_{\text{bot}} \)) with the smaller disk.(c) Use your two expressions to find the angular acceleration of the smaller disk. Your answer should have \( m \), \( R \), and \( \tau_0 \) in it only. (Careful, the smaller disk does not have the same angular acceleration as the larger one.)**Diagram Explanation:**The diagram depicts two disks of differing sizes connected by a belt. The larger disk is on the left, with a radius four times that of the smaller disk on the right. The belt is tensioned over both disks, showing how forces are transferred between them.

Given: Mass of both disk = m Input torque = T0 Radius of large disk = 4R Radius of small disk = R To…

Problem 8 Another Gear Two disks are connected to one another with a belt as shown. Both disks have mass m but the larger one has radius 4R and the smaller has radius R. The larger disk is powered by a motor that produces a constant torque, To, in the counter- clockwise direction. (a) By using the rotational equivalent of Newton's laws on the larger disk show that the difference in the tension at the top with the tension at the bottom is: Thot = (70 - 2m Ra), 1 4R where a is the linear accleration of teelt. (b) Do the same (find Ttop - Thot) with the smaller disk. (c) Use your two expressions to find the gular acceleration of the smaller disk. You answer should have m, R, and 70 in it only. (Careful, the sr aller disk does not have the same angular acceleration as the larger one).

Problem 8 Another Gear Two disks are connected to one another with a belt as shown. Both disks have mass m but the larger one has radius 4R and the smaller has radius R. The larger disk is powered by a motor that produces a constant torque, To, in the counter- clockwise direction. (a) By using the rotational equivalent of Newton's laws on the larger disk show that the difference in the tension at the top with the tension at the bottom is: Thot = (70 - 2m Ra), 1 4R where a is the linear accleration of teelt. (b) Do the same (find Ttop - Thot) with the smaller disk. (c) Use your two expressions to find the gular acceleration of the smaller disk. You answer should have m, R, and 70 in it only. (Careful, the sr aller disk does not have the same angular acceleration as the larger one).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Work and Heat Transfer

It is generally related to thermal engineering which tells about the use, creation, conversion and transfer of heat energy between the systems. It is also considered that to transfer heat from one source to another, transfer of masses is also required. There are various mechanisms by which, transfer of heat takes place i.e. thermal conduction, convection, radiation or by change of phase. All these mechanisms have their own specific features which sometimes occur simultaneously within the same system.

Question

**Problem 8: Another Gear**

Two disks are connected to one another with a belt as shown. Both disks have mass \( m \) but the larger one has radius \( 4R \) and the smaller has radius \( R \). The larger disk is powered by a motor that produces a constant torque, \( \tau_0 \), in the counterclockwise direction.

(a) By using the rotational equivalent of Newton’s laws on the larger disk, show that the difference in the tension at the top with the tension at the bottom is:

\[ T_{\text{top}} - T_{\text{bot}} = \frac{1}{4R} (\tau_0 - 2mRa), \]

where \( a \) is the linear acceleration of the belt.

(b) Do the same (find \( T_{\text{top}} - T_{\text{bot}} \)) with the smaller disk.

(c) Use your two expressions to find the angular acceleration of the smaller disk. Your answer should have \( m \), \( R \), and \( \tau_0 \) in it only. (Careful, the smaller disk does not have the same angular acceleration as the larger one.)

**Diagram Explanation:**

The diagram depicts two disks of differing sizes connected by a belt. The larger disk is on the left, with a radius four times that of the smaller disk on the right. The belt is tensioned over both disks, showing how forces are transferred between them.

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