Tangential Force Calculator

Enter the angular acceleration, radius, and mass into the calculator to determine the tangential force.

• All Physics Calculators
• All Force Calculators
• Angular Force Calculator
• Tangential Velocity Calculator
• Tangential Acceleration Calculator

Tangential Force Formula

The tangential force calculator determines the linear force acting along the tangent of a circular path. In this calculator’s model, the force is based on the mass being accelerated, the angular acceleration, and the radius from the axis of rotation to the mass.

F_t = m \alpha r

This means tangential force increases directly with mass, angular acceleration, and radius. If any one of those values doubles while the others stay constant, the tangential force also doubles.

How the Calculation Works

Tangential force comes from linear acceleration along the circular path. The tangential acceleration at radius r is:

a_t = \alpha r

Applying Newton’s second law in the tangential direction gives:

F_t = m a_t

Combining the two equations produces the calculator formula:

F_t = m \alpha r

This is especially useful for rotating point masses, pulley rims, wheel edges, and similar systems where the radius to the force location is known.

Connection to Torque

Tangential force and torque are closely related. A tangential force applied at a radius produces torque about the axis:

\tau = r F_t

If torque is known, the equivalent tangential force at that radius is:

F_t = \frac{\tau}{r}

For a point mass, this is consistent with rotational dynamics because the moment of inertia is:

I = m r^2

How to Use the Calculator

1. Enter the angular acceleration of the rotating system.
2. Enter the mass being accelerated.
3. Enter the radius from the center of rotation to the mass.
4. Select the correct units for each value.
5. Read the resulting tangential force in newtons or pound-force.

Be careful to use the radius, not the diameter. The radius is the distance from the axis of rotation to the object or point where the force acts.

Example

If a 3 kg mass rotates at a radius of 5 m and the angular acceleration is 4 rad/s², then:

F_t = 3 \cdot 4 \cdot 5

F_t = 60 \text{ N}

So the tangential force required is 60 N.

Tangential Force vs. Centripetal Force

Tangential force is not the same as centripetal force. Tangential force changes the speed of the object around the circle, while centripetal force changes the direction of motion toward the center.

F_c = m \omega^2 r

In many rotating systems, both force components can exist at the same time: one along the tangent and one toward the center.

Unit Notes

The standard SI form of the equation uses kilograms, meters, and radians per second squared. If you are solving by hand and need to convert angular acceleration, these relationships are useful:

\alpha_{\text{rad/s}^2} = \alpha_{\text{deg/s}^2} \cdot \frac{\pi}{180}

\alpha_{\text{rad/s}^2} = \alpha_{\text{rev/min}^2} \cdot \frac{2\pi}{3600}

Keeping all inputs in compatible units prevents most calculation errors.

Common Input Mistakes

• Using diameter instead of radius.
• Mixing mass units and force units without conversion.
• Confusing angular acceleration with angular velocity.
• Using centripetal force when the problem asks for tangential force.
• Entering values that describe a rigid body problem when the formula assumes a point mass or equivalent mass at radius r.

When This Calculator Is Most Useful

• Wheel and pulley motion problems
• Rotating mass and rim-force calculations
• Introductory physics and engineering homework
• Estimating linear force from angular acceleration
• Checking force requirements at a known distance from an axis