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Rotational Kinetics

Problems

Defining Rotation and its Variables

Rotational Kinematics

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 2Π radians. Thus 100 revolutions corresponds to 200Π radians. Thus:

σ = = = 40Π rad/s = 125.7 rad/s

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:

α = = = 20 rad/s2

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

× = 3.98 revolutions

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

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