(a) The angular speed of Allen is 0.628 rad/s.
(b) The angular speed of Beth is 0.628 rad/s.
(c) The linear speed of Allen is 2.512 m/s.
(d) The linear speed of Beth is 1.256 m/s.
The given parameters;
- radius of the carousel, r = 4 m
- speed, ω = 1 rev per 10 seconds
- position of Allen from the center of the carousel, r = 4 m
- position of Beth from the center of the carousel, r = 2 m
The angular speed of Allen is calculated as follows;
[tex]\omega = \frac{1 \ rev}{10 \ s} \times \frac{2\pi \ rad}{1 \ rev} \\\\\omega = 0.628 \ rad/s[/tex]
The angular speed of Beth is calculated as follows;
[tex]\omega = \frac{1 \ rev}{10 \ s} \times \frac{2\pi \ rad}{1 \ rev} \\\\\omega = 0.628 \ rad/s[/tex]
Allen and Beth make the same number of revolutions every 10 seconds, hence their angular speed is the same.
The linear speed of Allen is calculated as follows;
[tex]v = \omega r\\\\v = 0.628 \ rad/s \times 4 \ m\\\\v = 2.512 \ m/s[/tex]
The linear speed of Beth is calculated as follows;
[tex]v = \omega r\\\\v = 0.628 \ rad/s \times 2 \ m\\\\v = 1.256 \ m/s[/tex]
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