Static Friction in Pure Rolling
In pure rolling, contact friction is static and its direction follows the required translational and rotational accelerations rather than automatically opposing centre-of-mass motion; its magnitude must satisfy |f| <= mu_s N.
Why this shows up in the exam
Driven wheels and pulled cylinders · Rolling under applied forces at different heights · Checking no-slip conditions on inclines
Learn the idea
Static friction supplies whatever torque is needed for no slip, up to its limiting value. Static friction supplies whatever torque is needed for no slip, up to its limiting value. Start from a clear axis, origin, body, and reference frame; the geometry and constraints then decide which rotational law is safe to use.
🧠 Memory hook: Static friction prevents relative slip; it need not oppose the centre's motion.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F_cm = M a_cm — Translation equation including static friction.
- tau_cm = I_cm alpha — Rotation equation driven by contact and applied forces.
- |f| <= mu_s N — Feasibility condition for no slipping.
How to approach it
- 1Assume a friction direction
- 2Solve force, torque, and rolling equations
- 3Let the sign correct direction and verify the static limit
Common slip-ups that cost marks
- •Always drawing friction uphill
- •Setting f=mu_s N before impending slip
- •Ignoring torque of an off-centre applied force
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Masses 1 kg and 3 kg lie at x = 0 and x = 4 m. Find the x-coordinate of their centre of mass.
More from Motion of System of Particles and Rigid Body
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The total linear and angular momentum of a system remains constant in the absence of external forces or torques, including during collisions and rotational motion.
Moment of inertia and radius of gyration
Moment of inertia quantifies how mass is distributed with respect to an axis of rotation, and the radius of gyration is a measure related to this distribution.
Torque and rotational equilibrium
Torque is the rotational analogue of force, causing angular acceleration, and equilibrium occurs when the net torque on a body is zero.
Center of mass: definition and calculation
The center of mass is the point representing the mean position of the mass in a system, and can be calculated for discrete particles or continuous bodies.
Rotational kinematics and dynamics
Rotational kinematics describes the motion of rotating bodies, while dynamics relates torque, angular acceleration, and rotational kinetic energy.
Centre of Mass of Discrete Particles
For discrete particles, the centre-of-mass position is the vector sum of each mass times its position divided by total mass; this point governs translation even when the particles move relative to one another.