Answer:
a) Indeed, the linear speed of the ultracentrifuge is 0.524 kilometers per second.
b) Indeed, the linear speed of the Earth in its orbits about the Sun is approximately 30 kilometers per second.
Explanation:
The linear speed of the particle (), measured in kilometers per second, rotating in a circular pattern is calculated by the following formula:
(1)
Where:
- Radius, measured in kilometers.
- Angular speed, measured in radians per second.
Now we proceed to calculate the linear speed of each element:
a) Ultracentrifuge
If we know that and
, then the linear velocity is:
Indeed, the linear speed of the ultracentrifuge is 0.524 kilometers per second.
b) Earth
The Earth is 150 million kilometers away from the Sun and takes 365 days to complete one revolution around the Sun. First, we calculate angular speed of the planet:
(2)
Where is the period, measured in seconds.
If we know that , then the angular speed of the Earth is:
Now, we determine the linear speed:
Indeed, the linear speed of the Earth in its orbits about the Sun is approximately 30 kilometers per second.