16.103 (Rigid Body F=ma, General Plane Motion)
A drum of 60 mm radius is riveted to a disk of 120 mm radius. The disk
and drum have a combined mass of 6 kg and radius of gyration, kG, of
90 mm. A cord is wrapped around the inner drum and is pulled with force P
= 20 N in the direction shown. (The cord unwraps from the drum as the
spool rolls to the right). If the disk rolls without slipping, please
determine:
(a) The angular acceleration, a, of the disk.
(b) The acceleration, aG, of the mass center at G.
(c) The minimum value of the coefficient of friction, m,
consistent with this motion.
Comments/Hints:
1. Calculate IG = .0486 kg-m2.
2. Draw a FBD and a KD. On the KD are maG and IGa
terms.
3. Sum forces in the x and y directions and equate to ma terms.
4. Sum moments about G and set equal to IGa.
5. You need a kinematics equation: For a wheel that is not
slipping, aG = ra = 0.12a.
6. Solve for: a = 26.7 rad/sec2;
aG = 3.2 m/s2; F = 0.8 N (very small!).
7. The required m = (F/N)calculated
= 0.0136.