**Problem : **

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.

**Problem : **

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:

**Problem : **

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:

**Problem : **

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

× = 3.98 revolutions

Thus the merry-go-round revolves about 4 times in that period.
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