Kinetics of Rigid Bodies
Using the mass center G
Frictional Rolling Problems
Special Case: Pure Rotation
∑ F = ma
∑F =0
∑M
∑M
G
G
= I Gα
Special Case: Pure Translation
⇒α = 0
∴
∑ F = maG
∑M
G
=0
G
„
Rolling can be
considered as the sum:
‰
So
= I Gα
Using a fixed point O
∑ F = ma
Of Pure Translation
∑ F = maG
applies
‰
And Pure Rotation
G
∑M
O
= I Oα
So
∑ M G = I Gα
applies
Use of Normal & Tangential
Coordinates is useful
Let’s examine the case of a uniform disk (or wheel, or
cylinder, or sphere, etc.) moving on a flat horizontal
surface that is subjected to a constant horizontal force.
The 60 lb wheel has a mass moment of inertia of
IG = 1.20 slug-ft2. If a 35 ft-lb torque is applied
to the wheel, determine the acceleration of the
mass center G. The wheel rolls without slipping.
We have 3 equations and 4
unknowns (F, N, α, and aG).
We need one more equation.
∑ F = maG
∑ Fx = P − F = maG
∑ Fy = N − mg = 0
∑ M G = I Gα
− Fr = − I Gα
If NO slipping,
??? "o':-0 ':"""
aG = rα
If slipping,
F = μk N
1
The 8.0 kg spool has a mass moment of inertia of
IG = 1.35 kg-m2. If the ropes have negligible
mass, determine the acceleration of the mass
center G. Assume 3 SF.
A 16 lb bowling ball is cast horizontally onto a lane such
that ω = 0 and its mass center has a velocity of v = 8.0 ft/s
as shown. Determine the distance the ball travels before it
begins to roll without slipping. The coefficient of kinetic
friction is μk = 0.12 and assume 3 SF.
A 16 lb bowling ball is cast horizontally onto a lane such
that ω = 0 and its mass center has a velocity of v = 8.0 ft/s
as shown. Determine the distance the ball travels before it
begins to roll without slipping. The coefficient of kinetic
friction is μk = 0.12 and assume 3 SF.
2