Given the three circles below, which one best represents an angle of exactly one radian?

Explain where the equation for the circumference of a circle comes from in the context of the ratio cited in level one. In other words, why does the circumference equal 2*pi*r?

Pi is simply a number, but one that is special. Explain what kind of a number it is, why it is signifcant, and why it is given its own symbol.

An apple pie is cut into eight equal pieces. What angle in degress and radians are the pieces cut into? Note: if you use the visual method for determining the radians, you would have to use a full circle, which is 2pi, as opposed to the half circle we used in class. (45 degrees; pi/4 radians)

Suppose three slices were taken. What angle is left in degrees and radians? (225 degrees; 5pi/4 radians)

How many radians does the second hand of a clock turn through in 30 s? Express your answer in terms of pi.

In 90 seconds?

In 45 seconds?

For Honors physics only: Convert the following angles from degrees to radians using the conversion equation: 120 degrees, 240 degrees, 300 degrees, and 330 degrees.Pick one of the angles and draw the visual representation. (2pi/3 rad, 4pi/3 rad, 10pi/6 rad, 11pi/6)

Convert the following angles from radians to degrees using the conversion equation: 5pi/6 rad, 7pi/6 rad, 3pi/2 rad, and 9pi/4 rad. (150 degrees, 210 degrees, 270 degrees, and 405 degrees)

2. If a wheel were spinning counterclockwise, would omega point into the paper, or out of the paper? Explain why.

If the wheel's rate of rotation was decreasing, in what direction would alpha (angular acceleration) point: into the paper or out of the paper? Explain why using what you learned last semester.

What would have to be true for the direction of both omega and alpha, if the wheel's rate of rotation was increasing?

3. Explain why point B on the rotating disc below is able to have (and has to have) a larger tangential speed than point A. Draw on the diagram to illustrate your answer as well.

As a result of this relationship, how much larger would a person A's tangential velocity be compared to person B's if person A was located 9 meters from the center of a large merry-go-ground and person B was 3 meters from the center?

Centripetal force has an inverse relationship with radius, which means the closer one gets to the center of the rotating object (radius decreases), what happens to the force: does it increase or decrease?

This seems to bring up an apparent contradiction: in level one, it is established the closer one is to the center, the slower their tangential velocity gets, but the last level established the centripetal force increases when one gets closer to the center. Since physics cannot have any contradictions, there is an answer that eliminates the contradiction. There are two different assumptions made for the two different situations. For example, the assumption made for the relationship between the tangential velocity and how far one is from the center is stated in the parentheses in level one. What is the assumption made for the centripetal force situation?

4. Fill in the chart below:

In what ways are they different?

Give an example where moment of inertia is present in your everyday life:

A solid sphere (I = 2/5mr^2) rolls down a hill with a hollow sphere (I = 2/3mr^2). Which one would make it down the hill first: the solid or hollow sphere? Explain why.

What is the relationship between an object's moment of inertia and its radius?

If the radius of a spinning crank were doubled, how much would its moment of inertia increase? (Four times)

If the radius were decreased by one third, how much would the moment of inertia change? (Decrease by a factor of one ninth)

If you were designing a motor that included spinning wheels driven by rubber belts, why is the size of the wheel (its radius) important to consider? In other words, what do you have to consider if you wanted to make the radius larger?

It requires energy (therefore work) for an object to rotate, just like it requires energy (and also work) to make an object move in a straight line. Two cars at the top of a steep hill covered in ice share the same potential energy. One will slide down (with the breaks locked), and the other will roll down. In this situation, the only force doing work is gravity. Explain why the car that slides will make it down the hill first, keeping in mind that the total energy must stay the same, which means the energy at the top of the hill must equal the energy at the bottom of the hill.

  5. Torque is the angular counterpart to force. However, it is not like velocity and omega, because those two quantities are directly related. Explain how the relationship between torque and force is more like inertia and moment of inertia.

If the net torque on an object is zero, there are two possibilities for its rotation. State them:

What Law of Motion is this?

Explain why torque and alpha always point in the same direction based on what you learned last semester:

Explain why it is easier to stay balanced on a bicyle when it is moving as compared to when it is at rest.

Explain why a figure skater's rotational speed increases as she brings her arms in closer to her body using the figure below:

For Honors physics only:

Give the equation for Newton's Second Law for angular motion:

Last semester you learned that Impulse (force times time) is equal to an object's change in momentum. Is there an angular equivalent of Impulse, and if so, how would the equation look?