Physics in Video Game Engines: Torque and Inertia

Have you ever wondered what makes a car in a racing game drift around a corner, or why a ball bounces realistically off the ground? That’s all thanks to physics in video game engines. Physics simulation is the backbone of believable interactions in games, making objects behave like they would in the real world.

Let’s break down some of the most fundamental concepts of physics in game engines—velocity, force, torque, and inertia

1. Velocity: The Speed and Direction of Motion

Velocity measures how fast an object is moving and in which direction. It’s represented as a vector with both magnitude (speed) and direction.

Formula:

v = Δx / Δt

Where:

• v is velocity
• Δx is the change in position
• Δt is the change in time

Example: A soccer ball rolling across the field has a velocity that describes how fast it’s moving and in which direction. Kicking the ball harder increases its velocity.

2. Force: What Causes Motion

Force causes an object to start moving, stop moving, or change its direction. Newton’s Second Law of Motion describes it as:

Formula:

F = m * a

Where:

• F is the force applied
• m is the mass of the object
• a is the acceleration

Example: When you push a box, you apply force to overcome inertia and move it. A heavier box requires more force to move it at the same acceleration.

3. Torque: Rotational Force

Torque is similar to force, but it affects rotational motion around an axis.

Formula:

τ = r * F * sin(θ)

Where:

• τ is torque
• r is the distance from the axis of rotation
• F is the applied force
• θ is the angle between the force and the lever arm

Example: Think about opening a door: pushing farther from the hinges (axis) makes it easier to rotate. Torque increases with distance from the axis. Or when you use a lever to move a heavy object.

4. Inertia: Resistance to Motion

Inertia describes an object’s resistance to changes in motion. For linear motion, inertia depends on the object’s mass. For rotational motion, it depends on the moment of inertia.

Formula for Moment of Inertia (Point Mass):

I = m * r^2

Where:

• I is the moment of inertia
• m is the mass
• r is the distance from the axis of rotation

Example: A spinning ice skater pulls their arms inward to reduce their moment of inertia and spin faster. Extending their arms slows them down. You can also simulate this if you have a spinning chair.

Physics in game engines is what breathes life into the virtual worlds we create. The principles of velocity, force, torque, and inertia aren’t just for physicists—they’re for every game developer building immersive, believable experiences.