__Angular Torque Calculator:__

__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/s^{2}) to determine the value of Angular torque, T_{a(N.m)}.

__Angular Torque Formula__

__Angular Torque Formula__

Angular torque, T_{a(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/s^{2}) in radian per second square.

Angular torque, T_{a(N.m)} = m_{(kg·m²)} * (r_{(m)})^{2} * α(rad/s^{2})

T_{a(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/s^{2}) = the angular acceleration in radian per second square, rad/s^{2}

__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/s^{2}) = 10 rad/s², r_{(m) }= 0.5m.

Angular torque, T_{a(N.m)} = m_{(kg)} * (r_{(m)})^{2} * α(rad/s^{2})

T_{a(N.m)} = 0.2 * (0.5)^{2} * 10

T_{a(N.m)} = 0.2 * 0.25 * 10

T_{a(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: T_{a(N.m)} = 2N.m, m_{(kg)} = 0.5 kg·m², r_{(m) }= 0.4m.

Angular torque, T_{a(N.m)} = m_{(kg)} * (r_{(m)})^{2} * α(rad/s^{2})

α(rad/s^{2}) = T_{a(N.m)} / m_{(kg)} * (r_{(m)})^{2}

α(rad/s^{2}) = 2 / 0.5 * (0.4)^{2}

α(rad/s^{2}) = 2 / 0.5 * 0.16

α(rad/s^{2}) = 25rad/s^{2}.