Pricing
103/3334–6FE Reference Handbook 10.4 · Dynamics · Rigid-Body Motion
1. Constant Acceleration2. Newton’s Second Law3. Work–Energy Principle4. No-Time Acceleration Equation5. Position–Time Equation6. Impulse–Momentum Principle7. Translational Kinetic Energy8. Normal (Centripetal) Acceleration9. Level-Ground Projectile Range10. Power11. Angular Form of Newton’s Second Law12. Relative Velocity13. Coefficient of Restitution14. Elastic Spring Energy15. Rigid-Body Rotation: Tangential and Normal Accel.16. Mass Moment of Inertia17. Conservation of Mechanical Energy18. Angular Impulse–Momentum19. Rolling Without Slip20. Polar / Path Normal–Tangential Acceleration21. Instantaneous Center of Zero Velocity22. Work of a Variable Force

Handbook formula

Rolling Without Slip

No-slip rolling means the contact point is instantaneously at rest: the body rotates about the contact point. Static friction does no work (no slip). Check μs N ≥ required friction or else it slips.

Radius
Angular acceleration

Step-by-step solved example

Wheel r=0.4 m, a_G=2 m/s², no slip. α?

TL
v = ωr with the contact at rest (IC at the ground).

  1. 1. Kinematic link

    a=rα → α=2/0.4=5 rad/s².

  2. 2. IC

    Instantaneous center at the ground contact.

Answer: α = 5 rad/s²

10 practice questions

0/10 correct

1.If the wheel slips, v and rω are

2.Work of static friction in pure rolling is

3.I about contact C by parallel axis is

4.v_G=8 m/s, r=0.5 m, no slip: ω =

5.Required friction for a disk accelerated by M at the hub depends on

6.Hoop I=mR² rolling down a height h: v =

7.Sphere I=2/5 mR² is faster than a hoop because

8.Point at the top of a rolling wheel has speed

9.Impending slip uses

10.a_G of rolling down θ (no slip, disk ½mR²) is