Question

1)A particle of mass m and initialspeedv0 collideswith and sticks to the edge of a

uniform solid disk of massM and radius R. If thedisk is initially at rest and is

pivoted about africtionless axle through its center(perpendicular to thepage):

(a) find the angularvelocity of the system afterthe collision.

(b) find how much energyis lost in thecollision.

2)A uniform solid disk of radius Rand massM is free to rotate on a frictionless

pivot through a point onits rim. If it starts fromrest with its center at thesame

height as thepivot:

(a) What is its angularacceleration both at thestart and when itscenter is directly

below the pivot?

(b) What is its angularvelocity both at the startand when itscenter is directly below

the pivot ?

(c) What are thecomponents of the reaction force ofthe pivot on the disk both atthe

startand when its center is directlybelow the pivot ?

3)Suppose that we hang from itsrim a hoopof diameter 30cm and mass .4kg and set it swinging.

a)Define the moment of inertiaformally andfind it for the given hoop. b) Statethefundamental

dynamical equation ofrotational motion.c) Now applythe equation to this problemcarefully

inserting all thespecifics as far as you know them.d) In thelimit of small displacements solvethe

equation of motion andidentify theperiod of the motion.

4) A spool ofstring of radius Rand mass M is unwound under a constant forceF.

Assuming that the spoolrollswithoutslipping:

(a) What is theacceleration of the center of mass?

(b) What is its center ofmass velocity afterrolling a distance d ?

(c) What is thefrictional force?

5A ballistic pendulum consists ofa simpleuniform rod of mass M and length L hanging vertically atrest.A

blob of putty of mass m isshot horizontally atspeed v so that it collides with and sticks tothe lower hanging

end of the rod at itslowest point. Find the maximumangle that the rod now swingsthrough as it swings

upward recoiling.