The Velocity of Their Center of Mass Will Be Zero

KEY - Angular Momentum

1.  A child stands on the edge of a rotating playground merry-go-round (the hand driven type). He then starts to walk toward the center of the merry-go-round. This results in a dangerous situation. Why?

As the child walks towards the center of the merry-go-round, the moment on inertia of the merry-go-round will decrease (I=mr2). Since angular momentum is conserved, if the moment of inertia decreases then the angular speed of the merry-go-round must increase (L=Iw). This causes a dangerous situation because the child may slip.

2.  Two ice skaters that weight the same skate towards each other with the same speed on parallel paths. As they pass each other they link arms.

a.  What is the velocity of their center of mass as they link arms?

The velocity of their center of mass will be zero.

b.  What happens to their initial, linear kinetic energy (remember, energy is always conserved)?

Their linear KE turns into rotational KE as they start to spin around their center of mass (their linked arms)

3.  What is the angular momentum of a 2.0 g particle moving counterclockwise (as viewed from above) with an angular speed of 5p rad/s in a horizontal circle of radius 15 cm? (Give magnitude and Direction)

4.  A 10-kg rotating disk of radius 0.25 m has an angular momentum of 0.45 kgm2/s. What is the angular speed of the disk? (1.4 rad/s)

5.  A small ball at the end of a string that passes through a tube is swung in a circle (like in the Centripetal Force Lab). When the string is pulled downward through the tube, the angular speed of the ball increases.

a.  Why does the angular speed increase? (Don’t say because you pulled on the string)

As the string is pulled, the radius decreases which decreases the moment of inertia (I=mr2). Since angular momentum is conserved, if the moment of inertia decreases, then the angular speed must increase (L=Iw)

b.  If the ball is initially moving at 2.8 m/s in a circle with a radius of 0.30 m, what will be its tangential speed if the string is pulled down to reduce the radius of the circle to 0.15 m? (neglect the mass of the string) (5.6 m/s)

6.  An ice skater spinning with outstretched arms has an angular speed of 4.0 rad/s. She tucks in her arms, decreasing her moment of inertia by 7.5%

a.  What is her resulting angular speed? (4.3 rad/s)

b.  By what factor does the skater’s kinetic energy change? (KE = 1.1KEo)

c.  Where does the extra kinetic energy come from?

Energy is added to the system as the skater does work to pull her arms inward.