Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Lecture 37

Exam: from 6 pm to 8 pm

Circular Motion

rdt

drar

dt

rda

maFmaF

r

rr

2;

;

22

2

y

x

r

ri

i

rirr

r

dt

drV

dt

drVr ;

dt

d

dt

d ; Ra

Quiz from Nov. 16

The block of mass M is placed on a rotating platform, a distance L from the center. The coefficient of friction between the block and the platform is .What is the largest constant value that can have before the block starts slipping?

Ex.5

A wheel, with radius 0.5 m and moment of inertia 50 kg m2 about its center, rotates about a frictionless axle with angular velocity 10 radians per second. A brake is applied which supplies a constant force to a point on the perimeter of the wheel of 10 N, tangent to the wheel and opposing the motion. How many revolutions will the wheel make before coming to rest?

Ex. 4A platform can rotate, without friction, about a vertical axle through its center with a moment of inertia, Ip. A small bug of mass m is placed on the platform at a distance b from the center, and the system is set spinning with angular velocity 0 (Clockwise as viewed from above).a) What is the total angular momentum of the system with the bug at rest on the platform?b) What is the total angular momentum if he runs in the opposite direction to the platform’s rotation?c) Is it possible for a little bug to stop the big platform from rotating?

Pr. 1

A bullet of mass m is fired in the negative x direction with velocity og magnitude V0, starting at x = x0, y=b. (y remains constant) What is its angular momentum, with respect to the origin, as a function of x? Neglect gravity.

Conservation of Momentum

extFdt

pd

)()(

)()(

,0,0

afterpbeforep

afterpbeforep

ConstpConstp

Constpdt

pdFIf

yy

xx

yx

ext

If the collision is perfectly elastic, the kinetic energy is conserved!

Two disks are spinning on a frictionless axle. The one on the left has mass M, radius RL, and moment of inertia about the axle IL. It is spinning with L in the direction shown. It is moving to the right with velocity of magnitude v0. The one on the right has mass M, radius RR, and moment of inertia about the axle IR. It is spinning with R in the direction shown. It is moving to the left with velocity of magnitude v0. When the two disks collide they stick together. What is the velocity and the angular velocity of the combined system after the collision?

)(][

;

;

2 rhrmriridt

drmrprL

dt

Ld

prL

Fr

r

exttot

Torque and Angular Momentum

Conservation of Angular Momentum

Help Session:

When: tonight at 7:10 pm

Where:202 James J. Cain Engineering/Physics Lab Building

Spence St.

Have a great day!

Hw: Be prepared for the test

Good luck!