When the speed of a shaft is doubled while maintaining the same power, what should be the new diameter to keep the maximum shear stress constant?

• A. 1/2 of the original diameter
• B. 1/sqrt 2 of the original diameter
• C. sqrt 2 of the original diameter
• D. 1/cu. rt of 2 of the original diameter

Answer: (D)

To determine the new diameter required to keep the maximum shear stress constant when the speed of a shaft is doubled while maintaining the same power, it’s essential to consider the relationship between shear stress, power, and shaft dimensions.

The power transmitted by a shaft can be expressed using the formula:

[ P = T \cdot \omega ]

where ( P ) is power, ( T ) is torque, and ( \omega ) (angular velocity) is proportional to the speed of the shaft. As the speed doubles, the angular velocity increases, which means that with constant power, the torque must decrease. The maximum shear stress (( \tau )) in the shaft is related to the torque (( T )) and the polar moment of inertia (( J )) according to the relation:

[ \tau = \frac{T \cdot r}{J} ]

where ( r ) is the radius of the shaft.

When the speed doubles, if we maintain constant power, we must decrease the torque in such a way that results in a specific relationship between the new diameter and the shear stress. The power equation rearranges to show that if speed (angular velocity) is doubled and power remains constant,