<< Chapter < Page Chapter >> Page >
  • Observe collisions of extended bodies in two dimensions.
  • Examine collision at the point of percussion.

Bowling pins are sent flying and spinning when hit by a bowling ball—angular momentum as well as linear momentum and energy have been imparted to the pins. (See [link] ). Many collisions involve angular momentum. Cars, for example, may spin and collide on ice or a wet surface. Baseball pitchers throw curves by putting spin on the baseball. A tennis player can put a lot of top spin on the tennis ball which causes it to dive down onto the court once it crosses the net. We now take a brief look at what happens when objects that can rotate collide.

Consider the relatively simple collision shown in [link] , in which a disk strikes and adheres to an initially motionless stick nailed at one end to a frictionless surface. After the collision, the two rotate about the nail. There is an unbalanced external force on the system at the nail. This force exerts no torque because its lever arm r size 12{r} {} is zero. Angular momentum is therefore conserved in the collision. Kinetic energy is not conserved, because the collision is inelastic. It is possible that momentum is not conserved either because the force at the nail may have a component in the direction of the disk’s initial velocity. Let us examine a case of rotation in a collision in [link] .

A bowling ball, just as it is striking the pins.
The bowling ball causes the pins to fly, some of them spinning violently. (credit: Tinou Bao, Flickr)
Figure a shows a disc m sliding toward a motionless stick M of length r pivoted about a nail, on a frictionless surface. In figure b, a disk hits the stick at one end and adheres to it, and the stick rotates, pivoting around the nail in a direction shown by the arrow in the clockwise direction and angular velocity omega.
(a) A disk slides toward a motionless stick on a frictionless surface. (b) The disk hits the stick at one end and adheres to it, and they rotate together, pivoting around the nail. Angular momentum is conserved for this inelastic collision because the surface is frictionless and the unbalanced external force at the nail exerts no torque.

Rotation in a collision

Suppose the disk in [link] has a mass of 50.0 g and an initial velocity of 30.0 m/s when it strikes the stick that is 1.20 m long and 2.00 kg.

(a) What is the angular velocity of the two after the collision?

(b) What is the kinetic energy before and after the collision?

(c) What is the total linear momentum before and after the collision?

Strategy for (a)

We can answer the first question using conservation of angular momentum as noted. Because angular momentum is size 12{Iω} {} , we can solve for angular velocity.

Solution for (a)

Conservation of angular momentum states

L = L , size 12{L=L'} {}

where primed quantities stand for conditions after the collision and both momenta are calculated relative to the pivot point. The initial angular momentum of the system of stick-disk is that of the disk just before it strikes the stick. That is,

L = , size 12{L=Iω} {}

where I size 12{I} {} is the moment of inertia of the disk and ω size 12{ω} {} is its angular velocity around the pivot point. Now, I = mr 2 size 12{I= ital "mr" rSup { size 8{2} } } {} (taking the disk to be approximately a point mass) and ω = v / r size 12{ω=v/r} {} , so that

L = mr 2 v r = mvr . size 12{L= ital "mr" rSup { size 8{2} } { {v} over {r} } = ital "mvr"} {}

After the collision,

L = I ω . size 12{L'=I'ω'} {}

It is ω size 12{ω rSup { size 8{'} } } {} that we wish to find. Conservation of angular momentum gives

I ω = mvr . size 12{I'ω'= ital "mvr"} {}

Rearranging the equation yields

ω = mvr I , size 12{ω'= { { ital "mvr"} over {I'} } } {}

where I size 12{I'} {} is the moment of inertia of the stick and disk stuck together, which is the sum of their individual moments of inertia about the nail. [link] gives the formula for a rod rotating around one end to be I = Mr 2 / 3 size 12{I= ital "Mr" rSup { size 8{2} } /3} {} . Thus,

Questions & Answers

2 how heat loss is prevented in a vacuum flask
Abdullah Reply
what is science
logical reasoning for a particular phenomenon.
I don't know anything about it 😔. I'm sorry, please forgive 😔
due to non in contact mean no conduction and no convection bec of non conducting base and walls and also their is a grape between the layer like to take the example of thermo flask
dimensions v²=u²+2at
Lagben Reply
what if time is not given in finding the average velocity?
Alan Reply
the magnetic circuit of a certain of the flux paths in each of the long and short sides being 25cm and 20cm reprectielectrove. there is an air gap of 2mm long in one the long sides if a flux density of 0.8weber/m is to produce in the magnet of 1500 turns..
Daniel Reply
How do you calculate precision
Sacky Reply
what module is that?
Chemisty 1A?
No it has something to do with measurements bro... What we did today in class
Tah bra honestly I didn't understand a thing in that class..when re your Tutorials?
Friday bro... But the topics we did are in this app... Just try to master them quickly before the test dates... Are you done with the Maths sheet
I eat ass
I'll work on the maths sheet tomorrow bra @Sacky Malyenge but I'll try mastering them
I'll eat your mom's ass with a side of tendies
@Fillemon Nanwaapo
lol, hush
There are very large numbers of charged particles in most objects. Why, then, don’t most objects exhibit static electricity?
Bilkisu Reply
Because there's an equal number of negative and positive charges... objects are neutral in nature
when a ball rolls on a smooth level ground,the motion of its centre is?
Mary Reply
what is electro magnetic field?
electromagnetic field is a special type of field been produced by electric charges..!!! like the word electro from Electricity and the word magnetic from Magnetism.. so it is more of a join field..!!!
Electromagnetic field is caused by moving electric charge
when a ball rolls on a smooth level ground,the motion of its centre is?
what's the relationship btw displacement and position
Declan Reply
displacement is the change of position 8======✊=D 💦💦
what is the meaning of elasticity
Pele Reply
is the ability of a material to or any object to expand to a limit point
this is about kinematics you bonk
what does emf/R mean
Eze Reply
What is work
Wisdom Reply
work is the product of force and perpendicular distance
Pls explain simple harmonic motion
Olaiya Reply
Any to and from motion of a fluid or any elastic object
a current of 5.5mA is flowing through a 3.3k resistor.compute th p.d developed across the resistor
Clifford Reply
A p.d of 24 volts exist across a 15 OHM'S resistor.calculate the current flowing the resistor
a current of 5.5mA is flowing through a 3.3kOHM'S resistor.compute th p.d developed across the resistor
solve it please
the so unit power is the watt(w)/joul/second (w1)/s
Jibo Reply
what is time
Jibo Reply
a measure of the duration of an event

Get the best College physics course in your pocket!

Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?