A body is in static equilibrium
Use force balance and torque balance, choosing a pivot that removes unwanted unknowns.
Watch for this: Zero torque alone does not ensure zero net force.
3 CHAPTERS / A CONNECTED READING ROUTE
Rotation & gravity
What changes when motion has an axis or an orbit?
The big picture
Rotation adds a geometric question to familiar mechanics: how far is each force or mass from the chosen axis? The same body has different moments of inertia about different axes, and a force can produce no torque about one point while producing torque about another.
Rolling combines translation with rotation. Orbits connect a central force to changing speed and energy. In both, begin with the physical constraints rather than treating a remembered formula as a universal rule.
What to read, and why
Start at the first stage if the subject is new. Otherwise, use the descriptions to find the missing step in your understanding. All chapter explanations are open; the labels identify chapters whose solutions and answer checks are also free.
STAGE 1
Choose the axis
Build torque and inertia about a consistent axis, then check equilibrium or angular acceleration.
STAGE 2
Test the contact
Relate centre-of-mass motion to rotation and verify that the required friction is available.
STAGE 3
Follow the orbit
Distinguish circular motion from an ellipse and track the roles of force, energy and angular momentum.
Choose a method before an equation
Use the physical conditions to narrow the choices. A formula becomes useful after you know why its model applies.
A body rolls without slipping
Apply the no-slip constraint only after checking the contact model.
Watch for this: Static friction is not automatically equal to its limiting value.
A satellite moves in an elliptical orbit
Use conserved energy and angular momentum between positions.
Watch for this: The circular-orbit speed relation does not apply at every point of an ellipse.
Try a complete free problem
These problems include the hints, worked reasoning and answer feedback. Attempt one before opening the solution.
One axis for the whole rotor →Advanced · Connect concepts · Free sampleTurn a wrench with an angled force →Intermediate · Apply a principle · Free sampleA torque starts a flywheel →Intermediate · Apply a principle · Free sampleGravity at one planet radius of altitude →Intermediate · Compare cases · Free sample
Browse all rotation & gravity problems →Before you move on
Close the worked examples and explain these aloud or on paper. If you need a formula, also state its assumptions.
- Explain how changing the torque origin changes individual torques while preserving a valid equilibrium calculation.
- Decide whether a proposed rolling solution requires more friction than the surface can provide.