A reaction wheel is a motor driven flywheel mounted inside a robot or spacecraft. When the wheel speeds up in one direction, the body around it feels a torque in the opposite direction. This lets a satellite point a camera, aim an antenna, or keep a robot balanced without wheels pushing on the ground.
The idea matters because precise orientation control is essential for space missions, self balancing robots, and stabilized instruments.
The physics comes from conservation of angular momentum and Newton's third law for rotational motion. The motor applies a torque to the flywheel, and the flywheel applies an equal and opposite torque to the chassis. By changing the wheel speed, the controller changes the body's angular velocity and angle.
Reaction wheels work best for fine control, but they can saturate when the flywheel reaches its maximum safe speed.
Key Facts
- Reaction wheel principle: speeding up the flywheel creates an opposite torque on the spacecraft or robot body.
- Angular momentum is L = Iω, where I is moment of inertia and ω is angular velocity.
- Motor torque is τ = Iα, where α is angular acceleration of the flywheel.
- For an isolated system, total angular momentum is conserved: Lwheel + Lbody = constant.
- Equal and opposite torques act between the wheel and body: τbody = -τwheel.
- A reaction wheel controls rotation about one axis, so three wheels are usually needed for full 3D attitude control.
Vocabulary
- Reaction wheel
- A spinning flywheel inside a robot or spacecraft used to create torque on the body by changing the wheel's speed.
- Torque
- A twisting effect that changes an object's rotational motion.
- Angular momentum
- A measure of rotational motion that depends on moment of inertia and angular velocity.
- Moment of inertia
- A measure of how strongly an object resists changes in its rotation about an axis.
- Saturation
- The condition when a reaction wheel has reached its speed limit and cannot provide more control torque in the needed direction.
Common Mistakes to Avoid
- Thinking the reaction wheel pushes on air or space is wrong because it works by internal torque exchange, not by pushing against the environment.
- Forgetting the opposite direction of the body rotation is wrong because the body torque is equal in size and opposite in direction to the wheel torque.
- Using linear momentum instead of angular momentum is wrong because reaction wheels control rotation, so L = Iω is the key quantity.
- Assuming a reaction wheel can spin faster forever is wrong because real motors and flywheels have maximum speeds, which can lead to saturation.
Practice Questions
- 1 A flywheel has moment of inertia 0.020 kg m^2 and angular acceleration 50 rad/s^2. What torque does the motor apply to the flywheel?
- 2 A reaction wheel changes speed from 200 rad/s to 500 rad/s. Its moment of inertia is 0.010 kg m^2. What is the change in angular momentum of the wheel?
- 3 A satellite needs to rotate clockwise to aim its camera. Explain which way the reaction wheel should accelerate and why.