Rotational Motion

Rotational Motion and Electric Motors

Moment and Torque

In rotational motion, torque represents the twisting force applied to an object about an axis of rotation. It causes angular acceleration and is analogous to force in linear motion. Mathematically, torque (τ) is calculated as the product of force (F) and the distance (r) from the axis of rotation:
τ=F⋅r

Relationship between Linear and Angular Velocity

The angular velocity (ω) of a rotating object is the rate of change of its angular displacement. It is related to linear velocity (v) by the equation:
v=r⋅ω, where r is the radius.

Angular Velocity

Angular velocity (ω) is the ratio of angular displacement (θ) to the time (t) taken to cover that displacement:
ω=△θ/△t​

Conversion between Radians and Degrees

Angular measurements can be in radians or degrees. To convert between the two, you can use the following formulas:

• To convert from degrees (D) to radians (R):
  R=π/180​⋅D

• To convert from radians (R) to degrees (D):
  D=180/π​⋅R

Characteristics of an Electric Motor - Operating Point

An electric motor is a device that converts electrical energy into mechanical motion. Its operating point is the combination of torque and speed at which the motor operates under a specific load. Key characteristics include:

• Torque-Speed Curve: This curve shows the relationship between torque and speed of the motor. It indicates the motor's performance at different operating points.

• Stall Torque: The highest torque a motor can generate when stationary. It occurs when the motor draws maximum current.

• No-Load Speed: The maximum speed a motor can achieve when no load is applied.

• Efficiency: The ratio of useful mechanical output power to the electrical input power. The operating point should aim for peak efficiency.

• Load Torque: The torque required by the load the motor is driving. The operating point must ensure that the motor can deliver the required torque.

• Speed-Torque Trade-off: Generally, increasing torque reduces speed and vice versa. Selecting an operating point involves a trade-off between torque and speed based on the specific application's requirements.

Conclusion

Understanding rotational motion and the characteristics of electric motors' operating points is essential for designing and optimizing mechanical systems. Balancing torque, speed, and efficiency is crucial for achieving desired performance in various applications.