PHYC10003 Chap.1 Forces, Friction and Rolling
Forces, Friction and Rolling
This chapter separates static friction, kinetic friction and pure rolling before any equation is chosen. It shows how the normal force depends on geometry, why friction opposes relative contact motion rather than centre-of-mass velocity, and how translational and rotational velocities combine around a rolling wheel. The final method links a friction force limit to signed acceleration and stopping distance.
The governing decision is the contact state. While surfaces stick, static friction supplies only the force needed to prevent relative motion, up to its limit. At impending slip the limit is reached; after sliding begins, the kinetic model applies. The normal force must come from balance perpendicular to the surface, so an incline or angled pull changes the available friction. Rolling adds another constraint.
Axle translation and rotation about the axle combine vectorially, giving a stationary contact point only when axle speed equals angular speed times radius. If those magnitudes differ, the contact slips and its relative velocity determines friction direction. In stopping problems, a declared positive axis keeps braking acceleration negative while stopping distance remains a positive magnitude at the end.
Useful checks include the drop from limiting static to kinetic friction, cancellation of mass in an ideal level-road braking limit, and the squared dependence of distance on initial speed. These ideas turn a coefficient formula into a sequence of physical tests rather than an automatic substitution.
What this chapter covers
- 01
Static friction as an adjusting force
- 02
Maximum static and kinetic friction
- 03
Normal force on level and inclined surfaces
- 04
Rolling without slipping
- 05
Contact-point velocity
- 06
Friction-limited braking
Worked example · free
Test pure rolling from axle and angular speed
- 1Calculate omega times radius as 6.4 m/s.
- 1Set the clockwise bottom-rim velocity opposite the axle velocity.
- 1Add the road-frame vectors to obtain zero at contact.
- 1Conclude that the motion satisfies pure rolling at that instant.
Key terms
- Normal Force
- A normal force is the contact force perpendicular to a surface.
- Impending Slip
- Impending slip is the threshold state where static friction has reached its limiting magnitude.
- Pure Rolling
- Pure rolling occurs when the contact point is instantaneously at rest relative to the surface.
- Angular Speed
- Angular speed is the rate at which rotational phase changes in radians per second.
- Stopping Distance
- Stopping distance is the displacement required to reduce speed to zero under a stated acceleration model.
Forces, Friction and Rolling FAQ
Is static friction always equal to its maximum value?
No. Static friction matches the tangential force needed to prevent relative motion until it reaches its maximum. Use an inequality during sticking and set it equal to its maximum only at impending slip. A smaller applied tangential force therefore produces an equally smaller static-friction response.
Why can friction point forward on a driven wheel?
Friction opposes the tyre's tendency to slip relative to the road. A driven tyre tends to push the road backward at contact, so the road exerts forward static friction on the tyre.
Why is the bottom of a rolling wheel instantaneously still?
In the road frame, the axle translation points forward while the bottom rim's rotational velocity points backward with equal magnitude under pure rolling. Their vector sum is zero at that instant.
Exam move
Draw a free-body diagram and label the intended contact motion before choosing a friction model. Begin each friction problem with a state test: sticking, impending slip, sliding, or pure rolling. During sticking, calculate the friction required by the other equations and compare it with the maximum available value. Use equality only at the threshold.
During sliding, use the kinetic model and point the force against relative contact motion. Rework level-surface examples with an angled pull, an angled push, and an incline so that the normal force is derived from vertical or perpendicular balance instead of replaced automatically by weight. Practise switching between wheel-centred and road frames. In the wheel-centred frame, mark tangential rim velocities from angular motion.
In the road frame, add axle translation to those vectors and verify the bottom, centre, and top velocities separately. If axle speed and angular speed times radius differ, use the contact-point result to determine the direction of slip rather than imposing the rolling constraint. For braking, declare the positive axis along initial motion and keep acceleration negative through the signed kinematic equation.
Predict whether greater friction should shorten or lengthen the stop before calculating. Then check that mass cancels in the ideal level-road limit and report distance as a positive magnitude only after the signed equation is complete. Build a mixed set where the question changes just one condition, such as pull angle, coefficient, initial speed, or wheel radius.
After each solution, state the model condition that could fail in reality. Finish by explaining aloud why static friction can point forward on a driven wheel and why the instantaneously stationary contact point does not mean the whole wheel is stationary.
Working through Forces, Friction and Rolling in PHYC10003? Sia is AskSia’s AI Physics tutor — ask any PHYC10003 Forces, Friction and Rolling question and get a clear, step-by-step explanation grounded in how PHYC10003 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
