PHYS 221 EXAM 2 REVIEW

Reminders: NO SI THURSDAY!!

Exam Overview“Approximately 1/3 of the problems will stress understanding of the physics concepts, whereas the remainder will be numerical problems to test ability to apply these concepts.” -Syllabus

27 Questions

Statistical Breakdown of Exam 2 26% Energy 17% Collisions (+Momentum) 46% Rotational (Center of mass, moment of

inertia, statics, angular momentum, torque) 10% Gravitational

Let’s put some analogies to work:Not knowing gravitation would be like losing 3 fingersNot knowing rotational is like losing a heart or both lungs

Energy Conservation of Energy

Conservative/Non-conservativePotential Energy

Springs Collisions Rotational Gravitational Force/PE

KE 2 types

Rotational Translational

Springs A 10 kg mass hits a spring at a speed of 50

m/s. The spring has k=30 N/m.How far will the spring be compressed?

What will the PE of the spring be when it is fully compressed?

What will the PE of the spring be when it is halfway compressed?

Conservation of Energy Find a method that works for you. What’s most important is that you fully understand your method, front and back. For me, I prefer doing one of two things:

If there’s no friction, I just write out the energy at the two points. If there is friction, I use =Work done by forces other than gravity

Define Mechanical Energy1. KE2. PE3. KE+PE

Given a PE graph or function, what is F? is just another symbol

for Where are the stable

and unstable equilibriums?

At what points is the force zero?

At what points is the force negative?

Where does the particle have maximum speed, if it’s released at x=4?

Recall that at equilibriums, the force is zero. AKA

You’re given What is F at x=-2?

Conservative Forces vs. Non-conservative Forces Conservative

Always associated with some PEWork doesn’t depend on path takenExamples: Gravity, Electrostatic

Not ConservativePE doesn’t existWork does depend on pathExamples: Friction, Air resistance

Collisions Momentum is a vector Conservation of momentum Impulse Elastic, Inelastic, Completely Inelastic

Deciding elasticityDo they tell you it’s elastic, inelastic, or

completely inelastic?

Yes

No

Does the problem say the objects stick

together after the collision?

Yes

It’s completely inelastic (KE not

conserved)

No

What is the of the collision?

0

Elastic

<0

Inelastic (could be completely inelastic, but doesn’t have to

be)

Is Momentum Conserved in a Collision In this course, YES, ALWAYS!

Impulse Impulse J: 3 ways to define

The impulse of A on B is equal and opposite to the impulse of B on A

A 5 kg ball hits a wall at 8 m/s and bounces back at the same speed. If the collision took 4 seconds, what is the average force done by the wall on the ball?

Rotational Moment of Inertia=Rotational Inertia:

(about some axis) Torque

(about some axis) (about some axis)

Angular momentum (about some axis)

Notice how everything angular is about some axis. Make sure that your choice of axes match. Center of Mass!!

Center of Mass!! Why is this important/grouped under

rotation?

=

Solve…

Mathematically…

IntuitivelyDo circular or non-circular go faster down

hills?

Angular momentum is the same for the two systems below about an axis through O.

Discrete/Continuous…which formula should I use?Discrete: Continuous:

(use equation sheet for this)Discrete: Continuous:

Worked exampleWhat is the angular momentum?

Parallel Axis Theorem (PAT):

Torque ( If net torque is zero, an object can still

be moving.In fact, the object can even be accelerating!However, the angular acceleration must be

zero, and the angular velocity must be constant.

Comparison between linear

and angular (Position) (Angular position)

(Linear velocity) (Angular velocity)   (Linear acceleration) (Angular acceleration)

I (Moment of Inertia) (Equation for force)  (Equation for torque)

(Equation relating force and torque) (Definition of linear momentum)

  (Definition of angular momentum)

(Definition of translational KE) (Definition of rotational KE) 

(Force-momentum relation) (Torque-angular momentum relation) 

(Impulse equation) (Angular Impulse equation) 

(Power and constant force, constant velocity relation)

(Power and constant torque, constant angular velocity relation) 

  (Work caused by force) (Work caused by torque)

Notice that there’s always an axis involved with every single rotational equivalent!

Statics Can be solved in 2 minutes Strategy: Generally, use conservation of

angular momentum first!

Both discrete and continuous!

Is Momentum Conserved? Is Angular Momentum Conserved?

Gravitation

Equation relating the period of a planet’s motion around a star of mass MNOTE: r is the distance between the two

masses, M is the mass of the object being orbited.

Examples: A planet is in a circular orbit around a star. The mass of the star is 5 * 1028 kg. If the period of the planet’s orbit is 1.00 * 105 s, then the orbital radius of the planet around the star is ____ m.

The centers of two small uniform spherical bodies are separated by a distance d and the magnitude of the attractive gravitational force of one on the other is F. If the distance between the centers of the bodies decreases to d/2, the magnitude of the force of one on the other becomes ____ .

A 1.53-kg mass hangs on a rope wrapped around a disk pulley of mass 7.07 kg and radius 66.0 cm. The rope does not slip on the pulley. What is the angular acceleration

of the pulley?

If the block has fallen 0.8 m, what is the speed of the block at that time? (Two ways to solve this)

Other Concepts Magnitude of Forces, vectors, etc…

Multi-Principle Problems

A

Trickier Problems