Enter the mass (kg), the radius (m), and the angular acceleration (rad/s^2) into the calculator to determine the Angular Torque.
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Angular Torque Formula
The following formula is used to calculate the Angular Torque.
Ta = m*r^2*α
- Where Ta is the Angular Torque (N-m)
- m is the mass (kg)
- r is the radius (m)
- α is the angular acceleration (rad/s^2)
To calculate the angular torque, multiply the mass by the radius squared, then multiply by the angular acceleration.
How to Calculate Angular Torque?
The following example problems outline how to calculate Angular Torque.
Example Problem #1
- First, determine the mass (kg). In this example, the mass (kg) is determined to be 10 .
- Next, determine the radius (m). For this problem, the radius (m) is measured to be 3 .
- Next, determine the angular acceleration (rad/s^2). In this case, the angular acceleration (rad/s^2) is found to be 40.
- Finally, calculate the Angular Torque using the formula above:
Ta = m*r^2*α
Inserting the values from above and solving yields:
Ta = 10*3^2*40 = 3,600 (N-m)
FAQ
What is the significance of angular torque in mechanical systems?
Angular torque is crucial in mechanical systems as it measures the tendency of a force to rotate an object about an axis, pivot, or fulcrum. It plays a vital role in determining the efficiency and performance of various mechanical devices, including engines, turbines, and even simple machines like levers and pulleys.
How does changing the radius affect the angular torque?
According to the angular torque formula (Ta = m*r^2*α), the torque is directly proportional to the square of the radius. This means that increasing the radius will significantly increase the torque, assuming mass and angular acceleration remain constant. Conversely, decreasing the radius will reduce the torque. This relationship is critical in designing mechanical systems for desired torque outputs.
Can angular torque be negative, and what does it signify?
Yes, angular torque can be negative. In the context of rotational motion, a positive torque accelerates an object in the counter-clockwise direction, while a negative torque accelerates it in the clockwise direction. The sign of the torque depends on the direction of the applied force relative to the rotation axis. Negative torque is often used in systems requiring controlled deceleration or in scenarios where rotation direction needs to be reversed.
