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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 11.7 Applications of Circular Motion

Activity 11.7.1. The Motion of the Moon.

Assume that the Moon goes around the Earth in a roughly circular orbit.

(a)

Sketch and label a picture of the orbit.

(b)

Describe where the Moon is located in as many different ways as you can.

(c)

Describe how fast the Moon is moving in as many different ways as you can.

(d)

Assume the Moon’s angular speed \(\omega_M\) is roughly constant. Determine each of the following as a function of time:
  1. Angular position \(\theta(t)\)
  2. Angular speed \(\omega(t)\)
  3. Angular acceleration \(\alpha(t)\)
  4. Centripetal acceleration \(a_c(t)\)

Activity 11.7.2. The Clock with Three Hands.

Each of the three \(10 \mathrm{~cm}\) radius hands on an analog clock (hour, minute, second) can be treated as having uniform circular motion. For the tip of each clock hand, find each of the following:
  • The period
  • The angular speed
  • The tangential velocity
  • The centripetal acceleration

Activity 11.7.3. Uniform Circular Motion Table.

An object that is moving with uniform circular motion follows a path that is circular while moving with a speed that is constant.

(a)

Draw a motion diagram for such an object that includes at least five different points. Your motion diagram should include, at each point: a representation of the object, a position vector, a velocity vector, and an acceleration vector.

(b)

Make a table with six columns:
  1. In the first (left-most) column, make a list of the following physical quantities of a particle moving around a circle at constant speed: (translational) position, (translational) velocity, (translational) acceleration, mass, net force, (translational) kinetic energy, and (translational) momentum.
  2. In the second column indicate if the quantity is a scalar or a vector.
  3. In the third column indicate if the quantity is constant or not constant.
  4. In the fourth column write the units for the quantity.
  5. In the fifth column write a symbolic definition of the quantity.
  6. In the sixth column, if the quantity is a vector, then write what is known about its direction.

A*R*C*S 11.7.4. The Coin on the Disc.

A small coin with mass \(m\) is placed on the edge of a disc of radius \(R\) that is rotating so that the speed of the coin is a constant \(v\text{.}\) The coefficient of static friction between the coin and the disc is \(\mu_s\text{.}\)
Tip 1.
Analyze and Represent: Draw a free-body diagram for the coin.
Tip 2.
Calculate: Find the force of static friction on the coin.
Tip 3.
Sensemake: Use special-case analysis to decide whether or not your answer makes sense.

Activity 11.7.5. The Merry-Go-Round.

You are riding a merry-go-round with a wild reputation. Below is your angular position vs. time.
Figure 11.7.1. Angular position vs. time for a merry-go-round.
Describe your experience on the merry-go-round using words, equations, and graphs.
Answer.
Figure 11.7.2. Angular speed vs. time for a merry-go-round.

Activity 11.7.6. Swing in a Circle.

A ball on a string with mass \(m\) is swung so that it moves in a vertical circle of radius \(r\text{.}\) The speed \(v\) of the ball is the same at the top of the circle and at the bottom of the circle.

(a)

Draw free-body diagrams for the ball at the top and bottom.

(b)

At the top, is the magnitude of the tension greater than, less than, or equal to the magnitude of the gravitational force on the ball? Explain your reasoning.

(c)

At the bottom, is the magnitude of the tension greater than, less than, or equal to the magnitude of the gravitational force on the ball? Explain your reasoning.

(d)

Find an expression for the tension in the string at the bottom.
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