Answer:
(i) The angular speed of the small metal object is 25.133 rad/s
(ii) The linear speed of the small metal object is 7.54 m/s.
Explanation:
Given;
radius of the circular path, r = 30 cm = 0.3 m
number of revolutions, n = 20
time of motion, t = 5 s
(i) The angular speed of the small metal object is calculated as;

(ii) The linear speed of the small metal object is calculated as;

Answer:
The weights are 1 kg, 3kg, 9kg and 27kg.
Explanation:
The weights are 1 kg, 3kg, 9kg and 27kg.
1+3+9+27= 40
27+9+3= 39
27+9+3-1=38
27+9+1=37
27+9=36
27+9-1=35
27+9+1-3=34
27+9-3=33
27+9-3-1=32
27+3+1=31
27+3=30
27+3-1=29
27+1=28
27
27-1=26
27+1-3=25
27-3=24
27-3-1=23
27+3+1-9=22
27+3-9=21
27+3-9-1=20
Like this all the weights from 1 to 40 kg can be made using 1,3,9 and 27 kg.
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This question is a very good one indeed! I am very happy you asked it. I would first like to say that, although energy is important, our planet is more so. That is why I feel like we should always try to explore ideas that are both useful to the human race but also useful in protecting our environment because what is the use in having energy if we will not be able to use it. That is why I feel that we should try at types of energy like solar and wind. The problem is finding ways that are less expensive and more efficient. For example, creating a wind energy system that creates a sizeable about of energy and also is not too expensive and hard to make like the wind turbines of nowadays. Also what comes into question is the effect of these ideas and I feel that although some of these may have harmful effects, they must be used. One thing though is that I do not agree in expanding on our oil and gas exploration because it has so many bad effects to our environment that it is hardly worth it. If we can find alternatives in these other sources, like many states in the USA are trying to do, then we will be able to move much faster in technology and also help protect our lovely planet.