Rotational Dynamics 2 Angular Momentum

Workshop Tutorials for Biological and Environmental Physics MR10B: Rotational Dynamics II

A. Qualitative Questions:

1. Global warming is an important issue. Many scientists believe that some of the ice in the arctic and antarctic will melt due to increasing temperatures over the next few decades. This will have many effects, such as decreasing sea temperature and increasing water levels. As the ice melts the water will be redistributed such that there will more water near the equator. a. What effect would this have on the moment of inertia of the Earth? b. How will this effect the length of a day?

2. One of the most popular forms of entertainment in the world is sport, and millions of dollars are spent developing better tennis racquets, lower friction swimming suits, harder to detect performance enhancing drugs and more efficient bicycles. As a professional physicist you’ve been called in by the Australian Institute of Sport to help them design a better bicycle wheel. There are two designs that they’re investigating. The first is a solid wheel of uniform density, and the second is a spoked wheel with very light spokes so that virtually all the mass of the wheel is at the rim. Both wheels have the same mass and radius. a. For a given translational velocity, assuming no slipping, which will be greater for the solid wheel; its translational kinetic energy or its rotational kinetic energy? b. What about for the spoked wheel at the same translational velocity? c. Which wheel will you recommend that they use and why?

2 2 (note: Idisc = ½ MR , Ihoop = MR )

B. Activity Questions:

1. The rotating stool Sit on the stool and start rotating with equal weights held in your hands. Start with the hands in close to your chest and slowly stretch your hands outwards. What do you observe? What happens when you pull them back in again? Why?

2. Bicycle wheel Spin up the bicycle wheel. What do you feel when you try to tilt the wheel? Carefully hand the wheel to someone sitting on the rotating stool. What happens when they tilt the wheel? Why?

3. Falling cats The diagram on display shows how a cat can rotate itself around so that it always lands on its feet. Sit on the rotating stool and see if you can turn yourself around the way a cat does. How is it possible to do so without violating conservation of angular momentum?

The Workshop Tutorial Project –MR10B: Rotational Dynamics II 125 C. Quantitative Questions:

1. A merry go round can be described as a horizontal platform in the shape of a disc which rotates on a frictionless bearing about a vertical axis through its centre. The platform has a mass of 150 kg, a radius of 2.0 m and a rotational inertia of 300 kg.m2. A 60 kg student walks slowly from the rim of the platform toward the centre. If the angular speed of the system is 1.5 rad.s-1 when the student starts at the rim, what is the angular speed when he is 0.5 m from the centre?

2. There are two competing forces in stars which for most of a stars existence roughly balance. One is the gravitational force which pulls the atoms and subatomic particles in towards each other. The other is an outward pressure due to the thermal energy of the particles, which bump against each other. As the nuclear processes in a star slow down the star begins to cool, and gravity becomes stronger than thermal pressures. a. What happens to the star when it runs low on nuclear fuel? b. What happens to the star’s moment of inertia? The surface of our sun rotates at about one revolution per month, although being made of gas it rotates more slowly at the equator than at the poles. It has a mass of 2  1030 kg and a radius of 1.4 million kilometres. c. Assuming that the whole sun rotates at one revolution per month, what is the angular momentum of the sun? Old collapsed stars, called neutron stars, can rotate at speeds up to 800 revolutions per second. d. By how much would our sun have to collapse to spin at this speed?

126 The Workshop Tutorial Project –MR10B: Rotational Dynamics II