Question 1. A student watches a spinning playground carousel. It consists of a uniform disk of mass 100 kg and radius 150 cm. The edge of the carousel is moving with a speed of 3 m/s when the student jumps on, landing on the edge (150 cm from the centre). The jump is in the radial direction (no tangential velocity). The student has a mass of 59 kg.

a) What is the angular velocity of the carousel immediately after the student jumps on? Assume that all of her mass is concentrated at a single distance, 150 cm from the centre of the carousel. (5 marks)

b) Once the student jumps on, the carousel gradually comes to a stop. How much energy is dissipated in this process? (2 marks)

c) If the carousel comes to a stop via constant angular acceleration during a span of 10 seconds, what is the magnitude of the angular acceleration due to friction? (2 marks)

Question 2. (The radius of the Earth is approximately 6,400 km.)

a) How much energy is required to elevate a 100 kg satellite to a height of 1600 km above the Earth? (2 marks)

b) How much energy is required to put it in a circular orbit once it is there? (1 mark)

c) Which requires more energy: elevating the satellite or putting it into a circular orbit once it has been elevated? (1 mark)

Question 3. A spherical space capsule (treated as a hollow sphere) with mass of 160,000 kg and radius of 25 m is designed with thrusters on either side. During an orbit correction it fires its thrusters, each of which exerts a force of 2 MN.

a) During a routine correction, the thruster on one side of the craft fails. What angular acceleration does the spacecraft experience? (3 marks)

b) It takes 3 seconds to abort the manoeuvre and shut off the thruster, during this time, what angular velocity has the spacecraft attained? (2 marks)

c) What acceleration does someone standing on the inside surface of the spacecraft feel, and how does this compare to g? (In other words, this has created artificial gravity of how many g’s? For comparison, you may be interested to know that, if not trained for high g manoeuvres, people pass out when experiencing 4-6 g). (3 marks)

d) Had both thrusters worked, and the motion was translational not rotational, what acceleration (in terms of g) would the passengers have experienced? (1 mark)

Question 4.

Which is greater: the angular momentum of the Sun, or the angular momentum of Jupiter? (8 marks)

Hint: This is a Fermi problem; clearly lay out all assumptions that you make, and justify anything that you think requires justification. You may look up values for some quantities, but clearly state when you have done this. We are more interested in the structure and logic of your calculation that we are on the precision of your answer. You will be graded on this logical structure, and should therefore lay out your calculation very cleary (even using bullet points if you think this is appropriate).

Question 5.

On August 17th 2017, the LIGO and Virgo gravitational-wave detectors observed the merger of two neutron stars in a binary system. As the two stars orbited one another, they emitted gravitational waves and their orbit became closer. Below we show you the frequency of the gravitational waves observed in the detectors, with the gravitational-wave frequency on the vertical axis, and time on the horizontal axis, with the collision of the two neutron stars happening at time = 0. The bright curve in the figure is the gravitational-wave signal that indicates the famous ‘chirp’ as the gravitational-wave frequency increases.

Let’s assume that the two merging neutron stars both have a mass of 1.4 times the mass of the Sun (take the mass of the Sun to be 2 × 1030 kg).

Consider two points during the merger: A, 20 seconds before the merger and B, just after the merger when the two neutron stars merge to form another neutron star -for simplicity we will assume this has twice the mass of the original neutron stars and a radius of 10km.

The orbital frequency at A can be read of the figure above; it turns out the orbital frequency is twice the gravitational-wave frequency. Therefore, at point A, let’s take the orbital frequency as 20 Hz. Let’s take the spin frequency of the final neutron star (point B) to be 500 Hz.

1) Calculate the orbital rotational energy at A. (6 marks)

2) Calculate the rotational energy of the body at B. (3 marks)

3) Estimate the loss of energy, and comment on where this energy went. (2 marks)

note: i am aware some of these topics are extension from vce physics but if anyone could post some solutions so i could mark and correct mine urgently, it will be greatly appreciated.