12.1 Kinematics of Uniform Circular Motion

State the difference between angular velocity and linear velocity.

A moon is in a circular orbit r about a planet. The angular speed of the moon in its orbit is ω. The planet and its moon may be considered to be point masses that are isolated in space. 

r and ω are related by the expression 

      r³ω² = constant 

Io and Europa are moons that are in circular orbits around the planet Jupiter.  

Data for Io and Europa are shown in Fig 1.1.

Use the data from Fig 1.1. to determine the angular speed of Europa in its orbit around Jupiter.

Calculate the time period of Europa.

Determine the radius of the orbit of a moon that had double the linear speed of Io but a third of its time period.

Two children A and B hold both sides of a rope 70 cm long. Child A swings around child B in a circular path, as shown Fig 1.1.

Fig 1.1

Child B travels a full rotation in 1.5 s.

Show that the angular displacement, Δθ in this time is 37°.

Child A now swings child B round till they are making 5 revolutions every 2 seconds. 

Calculate the linear speed of child B. 

As the children are spinning anti-clockwise, the rope suddenly snaps at the position of child A and B shown in Fig 1.2.

Draw the direction child B will continue to travel in the instance the rope is snapped.