How Does Air Resistance Affect Power in Rotational Motion?

In summary, a sphere with a mass of 1.9 kg and a radius of 0.5 m is attached to a massless rod of length 3.0 m. The system rotates horizontally at a constant angular speed of 422 rev/min about an axis located at the opposite end of the sphere. After 167.0 s, air resistance is introduced and provides a force of 0.23 N on the sphere in the opposite direction of motion. Using the moment of inertia and angular acceleration equations, the angular acceleration is calculated to be 0.034306 rad/s^2. The final angular speed is determined to be 49.878 rad/s. Finally, the power provided by
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A sphere of mass 1.9 kg and radius 0.5 m is attached to the end of a massless rod of length 3.0 m. The rod rotates about an axis that is at the opposite end of the sphere (see below). The system rotates horizontally about the axis at a constant 422 rev/min. After rotating at this angular speed in a vacuum, air resistance is introduced and provides a force 0.23 N on the sphere opposite to the direction of motion. What is the power (in W) provided by air resistance to the system 167.0 s after air resistance is introduced? (Enter the magnitude.)
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Work
$$I_(new)=2/5mR^2+M(3.5)^2$$= 23.465
$$3.5F_f=I\alpha$$=.034306
$$\alpha=3.5F_f/I$$
$$\omega_0=2\pi/60*422rpm$$=44.19
$$\omega=\omega_0+\alpha*167$$=49.878
$$P=F_f*\omega$$=11.4719

What did I done wrong? Thanks
 
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$P = \tau \cdot \omega$
 

FAQ: How Does Air Resistance Affect Power in Rotational Motion?

What is angular power for a system?

Angular power for a system is a measure of the rate at which a system can rotate or turn. It is a vector quantity that takes into account both the magnitude and direction of the rotational motion. It is typically measured in units of watts (W) or horsepower (hp).

How is angular power calculated?

Angular power can be calculated by multiplying the torque applied to a system by its angular velocity. The formula for angular power is P = τω, where P is power, τ is torque, and ω is angular velocity.

What is the relationship between angular power and linear power?

Angular power and linear power are related by the distance from the axis of rotation. Angular power is proportional to the distance from the axis, while linear power is inversely proportional to the distance. In other words, the farther away from the axis of rotation, the more angular power is needed to achieve the same linear power output.

How does angular power affect the performance of a system?

Angular power plays a crucial role in the performance of a system, especially in rotating machinery such as engines, turbines, and motors. It determines the speed at which a system can rotate and the amount of work it can perform. A higher angular power generally results in better performance and efficiency of the system.

Can angular power be increased?

Yes, angular power can be increased by increasing the torque or the angular velocity of a system. This can be achieved by using a more powerful motor or by modifying the design of the system to reduce friction and increase efficiency. However, the maximum angular power a system can achieve is limited by its physical properties and the laws of physics.

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