Angular Torque Calculator:
Angular torque, often simply referred to as torque, measures the tendency of a force to rotate an object about an axis, fulcrum, or pivot. It is a crucial concept in physics and engineering, especially when dealing with rotational dynamics.
Enter the values of the mass moment of inertia, m(kg), radius or distance r(m) and the angular acceleration α(rad/s2) to determine the value of Angular torque, Ta(N.m).
Angular Torque Formula
Angular torque, Ta(N.m) in Newton metre is calculated by multiplying the mass moment of inertia, m(kg·m²) in kilogram meter square of an object, radius or distance r(m) in metre from the pivot point to the point where the force is applied and the angular acceleration α(rad/s2) in radian per second square.
Angular torque, Ta(N.m) = m(kg·m²) * (r(m))2 * α(rad/s2)
Ta(N.m) = Angular torque in Newton metre, N.m
m(kg) = the mass moment of inertia in kilogram, kg
r(m) = radius or distance in metre, m.
α(rad/s2) = the angular acceleration in radian per second square, rad/s2
Angular Torque Calculation:
A wheel with a mass moment of inertia of 0.2 kg·m² is required to achieve an angular acceleration of 10 rad/s². The effective radius where the force is applied is 0.5 meters. Determine the angular torque applied to the wheel.
Given: m(kg) = 0.2 kg·m², α(rad/s2) = 10 rad/s², r(m) = 0.5m.
Angular torque, Ta(N.m) = m(kg) * (r(m))2 * α(rad/s2)
Ta(N.m) = 0.2 * (0.5)2 * 10
Ta(N.m) = 0.2 * 0.25 * 10
Ta(N.m) = 0.5N.m.
A disk with a mass moment of inertia of 0.5 kg·m² experiences an angular torque of 2 N.m. If the effective radius of force application is 0.4 meters, calculate the angular acceleration of the disk.
Given: Ta(N.m) = 2N.m, m(kg) = 0.5 kg·m², r(m) = 0.4m.
Angular torque, Ta(N.m) = m(kg) * (r(m))2 * α(rad/s2)
α(rad/s2) = Ta(N.m) / m(kg) * (r(m))2
α(rad/s2) = 2 / 0.5 * (0.4)2
α(rad/s2) = 2 / 0.5 * 0.16
α(rad/s2) = 25rad/s2.