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Answer :
Final answer:
To convert 180 rpm to m/s at a radius of 330 cm, we first convert rpm to rad/s, then calculate the speed by multiplying this value by the radius. The final answer is 62.2 m/s.
Explanation:
To convert 180 revolutions per minute (rpm) to meters per second (m/s) at a radius of 330 cm (3.3 m), we first need to convert rpm to radians per second (rad/s). One revolution is equivalent to 2π radians, thus 180 rpm is equivalent to 180*2π/60 rad/s = 18.85 rad/s.
The speed of the rotation in m/s is then calculated by multiplying the angular velocity in rad/s by the radius in metres. So, 18.85 rad/s * 3.3 m = 62.2 m/s.
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Rewritten by : Jeany
The linear speed corresponding to 180 revolutions per minute (rpm) at a radius of 330 centimeters is approximately 62.2 meters per second (m/s).
1. Convert Radius to Meters:
Since the radius is given in centimeters, convert it to meters by dividing by [tex]\(100\)[/tex]:
[tex]\(330 \text{ cm} \div 100 = 3.3 \text{ m}\)[/tex]
2. Calculate Circumference:
The circumference of a circle can be calculated using the formula [tex]\(2\pi r\)[/tex], where [tex]\(r\)[/tex] is the radius.
So, the circumference is:
[tex]\(2\pi \times 3.3 \text{ m} = 6.6\pi \text{ m}\)[/tex]
3. Convert RPM to RPS:
To convert revolutions per minute (rpm) to revolutions per second (rps), divide by [tex]\(60\)[/tex]:
[tex]\(180 \text{ rpm} \div 60 = 3 \text{ rps}\)[/tex]
4. Calculate Linear Speed:
Multiply the circumference by the number of revolutions per second to find the linear speed:
[tex]\(6.6\pi \text{ m} \times 3 \text{ rps} = 19.8\pi \text{ m/s}\)[/tex]
5. Approximate [tex]\(\pi\)[/tex]:
Use [tex]\(3.14\)[/tex] as an approximation for [tex]\(\pi\)[/tex]:
[tex]\(19.8 \times 3.14 \approx 62.2 \text{ m/s}\)[/tex]
So, the linear speed corresponding to [tex]\(180\)[/tex] rpm at a radius of [tex]\(330\)[/tex] cm is approximately [tex]\(62.2\)[/tex] meters per second.
Complete question:
Convert 180 rpm to m/s, at a radius of 330 cm. The answer must be in m/s.
