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• Run Multiple Choice Generator at h:\shares\physics
• General College Physics:  Run Core Problems by giving the program 174 as your 'course'--enter this when asked for your 3-digit course number.   Do the problems for 11/03.
• University Physics:  Run Multiple Choice Generator for 201 and choose 'Calculus of Uniformly Accelerated Motion'.
• If you miss a problem be sure to click on Comment and explain what you do and do not understand about the question and the given solution.

Text Assignments:

General College Physics:  Chapter 8, Problems 7, 11, 17, 20, 23, 24, 29, 33, 38

University Physics:  Chapter 9, Problems 58, 59, 64, 67, 71, 76, 79, 82

Run the following experiments:

Using a chain of two rubber bands, accelerate the meter stick across the tabletop using pullbacks of 1, 2, 3 and 4 cm.  Measure how far the meter stick slides in each case.

Using the same chain accelerate the meter stick, now constrained to rotate on a die, using the same pullbacks.  Measure the angular displacement and time required to come to rest.

Repeat for the 'loaded' meter stick.

Analysis:

Assume meter stick mass 60 grams, block have mass 40 grams each.

Assume coefficient of friction to be .15.  What KE results from each pullback?

What is the initial angular velocity of the meter stick in each case?

Graph the initial KE of the meter stick vs. its angular velocity.  Assume that the initial rotational KE for a given pullback is the same as the initial KE of the sliding meter stick.

The mass per unit length of the meter stick is about 1.2 grams / cm.

The mass density of the blocks is about .4 grams / cm^3.

Determine the moment of inertia of each rotating system.  From your information determine .5 I * omega^2 for the initial angular velocity omega_0 of the system.  Compare to your results for KE.

What is the angular velocity of an object which is moving at 6 m/s along the arc of a circle of radius 2 meters?

One rad / sec would be 2 m/s along the arc.

So 6 m/s along the arc is 3 rad / sec.

How fast is an object moving along the arc if its angular velocity on a circle of radius 5 meters is 4 radians / second?

1 rad / sec would give us 5 m/s along the arc.  So 4 rad / sec gives us 20 m/s.

Do all objects moving at the same angular velocity, in rad/s, have the same speed in m/s?

No.  The further from the axis of rotation the faster the object is moving.

How are the angular velocity (in rad / s) of an object moving on the arc of a circle and its speed (in m / s) related?

The relationship depends on the radius of the circle.  One radian of angular displacement is one radius of arc distance.

So arc displacement = angular displacement * radius, or `ds = `dTheta * r.

For obvious reasons velocity along arc = angular velocity * r, or v = omega * r, and

acceleration along arc = angular acceleration * radius or a = alpha * r.

Would the block on the meter stick have the same KE at an angular velocity of 1.5 rad / s, no matter where it is positioned on the stick?

No.  The further from the axis of rotation the greater the velocity and therefore the greater the KE.

Does every 1-cm segment of the meter stick have the same angular velocity as every other?

As long as the meter stick holds together, yup.

• Does every 1-cm segment have the same speed as every other? 

Nope.  The further from the axis the better.

• Does it have the same KE?

Nope.  Different speed, so different KE.

If I accelerate a 4-kg block with a 3 Newton force through a displacement of 2 cm, how fast will the block be moving?

.17 m/s.

If the block happens to be constrained to rotate in a circle of radius 25 cm then what will be its angular velocity?

.17 m/s on the arc of a .25 m circle implies angular velocity .17 m/s / (.25 m) = .68 rad/s.