Why this chapter matters
Many real systems rotate, and rotational analysis is needed for machines, structures, and everyday tools.
What you will learn
- Compute torque from force, lever arm, and angle with sign conventions.
- Apply rotational analogs of Newton's second law to rigid-body motion.
- Use translational and rotational equilibrium to solve static situations.
Lessons in this chapter
- Angular quantities and rigid rotationConnect angular displacement, velocity, and acceleration to linear motion at radius r.
- Torque and lever armDetermine torque direction and magnitude for multiple-force setups.
- Rotational inertia and dynamicsRelate torque, moment of inertia, and angular acceleration.
- Static equilibriumSolve for unknown forces using force and torque balance.
Study task
Analyze a balanced sign suspended by two cables. Write force-balance and torque-balance equations to solve cable tensions.
Chapter checkpoint
A 5.0 N force is applied perpendicular to a wrench 0.20 m from the pivot. What is the torque magnitude?
tau = rF sin(theta). With theta = 90 deg, tau = (0.20)(5.0)(1) = 1.0 N*m.