Rolling Without Slipping
Combined translation and rotation with the constraint v = w R, so total KE = Mv2/2 + I w2/2.
What is Rolling Without Slipping?
Combined translation and rotation with the constraint v = w R, so total KE = Mv2/2 + I w2/2.
Key formula / rule: Rolling constraint: v = wR, a = α R.
Key points
- Derive the acceleration of a body rolling down an incline.
- Compare rolling × of bodies with different mass distributions.
Common exam trap
Applying v = wR while the body is skidding.
Definitions
- Term
Rolling Without Slipping
- Meaning
Combined translation and rotation with the constraint v = w R, so total KE = Mv2/2 + I w2/2.
- Term
Rolling Without Slipping — explanation
- Meaning
The rolling constraint links the two motions and lets the energy be written as a single mass-dependent fraction. On an incline the acceleration g sin t/(1 + I/MR2) explains why a ring loses a race against a solid sphere.
Learning objectives
Derive the acceleration of a body rolling down an incline.
Compare rolling × of bodies with different mass distributions.
Formulae
- Key point
Rolling constraint: v = wR, a = α R.
- Key point
KEtotal = (1 + I/MR2) Mv2/2.
- Key point
Acceleration on an incline = g sin t/(1 + I/MR2), independent of mass and radius.
Prerequisites
PHY-U2-ROT-T2-S1-C1
PHY-U1-WEP-T1-S2-C2
Common mistakes
Applying v = wR while the body is skidding.
Omitting the rotational term from the total kinetic energy.
Keywords
Rolling
Without
Slipping
Practice preview
A solid sphere of mass M and radius R rolls without slipping down an inclined plane of angle theta. What is the acceleration of its center of mass?…
hard
For a rigid body rolling without slipping on a horizontal surface, which of the following conditions must be satisfied?…
easy
The total kinetic energy of a rigid body rolling without slipping is the sum of:…
easy