Unit & Physics

Free Torque & Rotational Dynamics Physics Calculator

Torque represents rotational force—the tendency of a force to rotate an object about an axis or pivot point. It is fundamental in mechanical engineering, automotive performance, and physics mechanics. Our free torque calculator allows students and engineers to compute rotational physics calculator metrics, solve calculate torque tau r f sin theta equations, and evaluate moment of inertia torque solver problems.

Torque & Rotational Dynamics Calculator

Calculate rotational force $\tau = r F \sin\theta$, angular acceleration $\alpha$, rotational kinetic energy, and horsepower.

Applied Force F (Newtons, N)

Lever Arm Radius r (meters, m)

Force Angle θ (Degrees, °)90° yields maximum torque

Moment of Inertia I (kg·m²)

Angular Velocity ω (rad/s)

Calculated Torque (τ)

75.00 N·m

= 55.32 lb-ft (Pound-Feet)

Angular Acceleration (α):30.00 rad/s²

Rotational Kinetic Energy:500.0 Joules

Rotational Power & Dynamics Summary

Mechanical Power Output

1500.0 W

(2.01 HP Horsepower)

Formula & Trigonometry

τ = 0.5m × 150N × sin(90°)

Effective Lever Arm: 0.500 m

Mathematical Formulas & Calculation Methods

Torque & Rotational Mechanics Formulas

Torque τ equals lever arm distance times force times sine of the angle.

Torque (τ) = r × F × sin(θ) Angular Acceleration (α) = τ / I | Power (P) = τ × ω

Worked Step-by-Step Examples

Example 1: Force F = 150 N applied at radius r = 0.5 m at angle θ = 90° with Moment of Inertia I = 2.5 kg·m²

"Calculate Torque, Angular Acceleration, and Power at ω = 20 rad/s."

Steps:

Torque τ = 0.5 m × 150 N × sin(90°) = 75.0 N·m.
In Imperial units: 75.0 N·m × 0.737562 = 55.32 lb-ft.
Angular Acceleration α = 75.0 / 2.5 = 30.0 rad/s².
Rotational Power P = 75.0 × 20 = 1,500 Watts (2.01 HP).

Result: Torque = 75.0 N·m (55.32 lb-ft) | α = 30.0 rad/s² | Power = 2.01 HP.

What is Torque & Rotational Dynamics Physics Calculator?

A torque calculator computes rotational force acting on a lever arm or rotating shaft.

A torque to power horsepower calculator converts mechanical rotational torque and RPM into Watts or Horsepower.

How to Use Torque & Rotational Dynamics Physics Calculator

1Enter Applied Force F (Newtons) and Lever Arm Radius r (meters).
2Enter Force Angle θ (Degrees, default 90°).
3Input Moment of Inertia I (kg·m²) and Angular Velocity ω (rad/s).
4Review Torque in N·m and lb-ft, Angular Acceleration, and Power Output.

Key Features

Calculates Torque in Newton-meters (N·m) and Pound-feet (lb-ft).
Computes Angular Acceleration α and Rotational Kinetic Energy.
Calculates mechanical power output in Watts and Horsepower (HP).

Benefits of Using Torque & Rotational Dynamics Physics Calculator

Essential tool for physics students, mechanical engineers, and automotive enthusiasts.

Eliminates manual trigonometric errors when forces are applied at non-perpendicular angles.

Practical Use Cases

Physics & Engineering Students

Solve rotational dynamics, lever arm, and torque physics homework.

Automotive & Mechanical Engineers

Calculate shaft torque, engine power, and bolt tightening force.

Frequently Asked Questions

What is the difference between Torque and Work?

Although both torque and work have units equivalent to Newton-meters (N·m), torque is a vector quantity representing rotational force at a point, while work is a scalar quantity representing energy transferred over a distance.

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