**Problem1 :**

Most planets orbit the sun in elliptical orbits. Do these planets exhibit rotational motion?

Rotational motion has two requirements: all particles must move about a fixed axis, and move in a circular path. Since the path of most planets is not circular, they do not exhibit rotational motion.

**Problem2 :**

A frisbee completes 100 revolutions every 5 seconds. What is the angular velocity of the frisbee?

Recall that = . We can assume that the angular velocity is constant, so we can use this equation to solve our problem. Each revolution corresponds to an angular displacement of 2

*Π*radians. Thus 100 revolutions corresponds to 200*Π*radians. Thus:*σ*= = = 40

*Π*rad/s = 125.7 rad/s

**Problem3 :**

A car, starting from rest, accelerates for 5 seconds until its wheels are moving with an angular velocity of 1000 rad/s. What is the angular acceleration of the wheels?

Again, we can assume that the acceleration is constant, and use the following equation:

*α*= = = 20 rad/s

^{2}

**Problem4 :**

A merry-go-round is accelerated uniformly from rest to an angular velocity of 5 rad/s in a period of 10 seconds. How many times does the merry-go-round make a complete revolution in this time?

We know that = . Since we want to solve for the total angular displacement, or

*φ*, we rearrange this equation:Δφ | = | Δt | |

= | Δt | ||

= | (10) | ||

= | 25 rad/s |

However, we are asked for the number of revolutions, not the number of radians. Since there are 2

*Π*radians in every revolution, we divide our number by 2

*Π*:

× = 3.98 revolutions