Gear A on the drive shaft of the outboard motor has a radius rÃ=9 in. and the meshed pinion gear B on the propeller shaft has a radius rg=53 in. The point P is located on the propeller's tip at a distance 4 in. from the neutral axis of the propeller's shaft. سب P B At the beginning of the propulsion, the drive shaft rotates with an angular acceleration a = A.t 2.0 rad.s 2 where t is in seconds.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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**Transcription:**

Gear A on the drive shaft of the outboard motor has a radius \( r_A = 9 \) in. and the meshed pinion gear B on the propeller shaft has a radius \( r_B = 53 \) in. 

The point \( P \) is located on the propeller's tip at a distance 4 in. from the neutral axis of the propeller's shaft.

At the beginning of the propulsion, the drive shaft rotates with an angular acceleration \( \alpha = A \cdot t \) rad\(\cdot \text{s}^{-2} \) where \( t \) is in seconds.

What must be the value of \( A \) to have, while starting from rest, \( v_P = 24 \, \text{in.}\cdot \text{s}^{-1} \) in 6 seconds?

**Diagram Explanation:**

The diagram illustrates the gear mechanism in an outboard motor. Gear A is connected to the drive shaft and has a smaller radius of 9 inches. A larger meshed pinion gear B is on the propeller shaft with a radius of 53 inches. Point \( P \) is at the tip of the propeller, indicating the location where velocity is being measured. The diagram shows smoke or water to suggest motion or propulsion produced by the rotation of the propeller.
Transcribed Image Text:**Transcription:** Gear A on the drive shaft of the outboard motor has a radius \( r_A = 9 \) in. and the meshed pinion gear B on the propeller shaft has a radius \( r_B = 53 \) in. The point \( P \) is located on the propeller's tip at a distance 4 in. from the neutral axis of the propeller's shaft. At the beginning of the propulsion, the drive shaft rotates with an angular acceleration \( \alpha = A \cdot t \) rad\(\cdot \text{s}^{-2} \) where \( t \) is in seconds. What must be the value of \( A \) to have, while starting from rest, \( v_P = 24 \, \text{in.}\cdot \text{s}^{-1} \) in 6 seconds? **Diagram Explanation:** The diagram illustrates the gear mechanism in an outboard motor. Gear A is connected to the drive shaft and has a smaller radius of 9 inches. A larger meshed pinion gear B is on the propeller shaft with a radius of 53 inches. Point \( P \) is at the tip of the propeller, indicating the location where velocity is being measured. The diagram shows smoke or water to suggest motion or propulsion produced by the rotation of the propeller.
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