__Acceleration to Torque Calculator:__

__Acceleration to Torque Calculator:__

Enter the values of angular acceleration, a(rad/s^{2}), mass, m_{(kg)} and radius, r_{(m)} to calculate the Acceleration to Torque, T_{(N.m)}.

__Acceleration to Torque Formula:__

__Acceleration to Torque Formula:__

The acceleration to torque formula is essential for determining the torque generated from accelerating a mass around a pivot point or axis.

Acceleration to Torque, T_{(N.m)} in Newton metres, is calculated by multiplying the angular acceleration, a(rad/s^{2}) in radians per second squared, by the mass, m_{(kg)} in kilograms, and by the radius, r_{(m)} in metres from the pivot point to the point where the mass is located.

Acceleration to Torque, T_{(N.m) }= a(rad/s^{2}) * m_{(kg)} * r_{(m)}

T_{(N.m)} = Acceleration to Torque in Newton metres, N.m.

a_{(rad/s2)} = Angular acceleration in radians per second squared, rad/s^{2}.

m_{(kg)} = Mass in kilograms, kg.

r_{(m)} = Radius in metres, m.

__Acceleration to Torque Calculation:__

__Acceleration to Torque Calculation:__

1. Suppose a disk with a mass of 10kg is mounted 0.5 metres away from a pivot point and is experiencing an angular acceleration of 2 rad/s^{2}. Determine the torque required to achieve this acceleration.

Given: m_{(kg)} = 10kg, a_{(rad/s2)} = 2 rad/s^{2}, r_{(m)} = 0.5m

Acceleration to Torque, T_{(N.m) }= a_{(rad/s2)} * m_{(kg)} * r_{(m)}

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

T_{(N.m)} = 10N.m.

2. A robotic arm is designed to rotate with an angular acceleration of 4rad/s^{2}. The arm’s effective radius from its rotation axis to its center of mass is 0.2 metres and the torque needed to achieve this acceleration is 4N.m. Calculate the mass.

Given: T_{(N.m)} = 4N.m., a_{(rad/s2)} = 4 rad/s^{2}, r_{(m)} = 0.2m

Acceleration to Torque, T_{(N.m) }= a_{(rad/s2)} * m_{(kg)} * r_{(m)}

m_{(kg)} = T_{(N.m) }/ r_{(m)} * a_{(rad/s2)}

m_{(kg)} = 4 / 4 * 0.2

m_{(kg)} = 5kg.