1500 rpm equals approximately 157.08 radians per second.
To convert revolutions per minute (rpm) to radians per second (rad/s), multiply rpm by 2π and then divide by 60. Since one revolution corresponds to 2π radians, this conversion accounts for the angular displacement in radians over time, giving a precise measure of angular velocity.
Conversion Formula
The formula to convert rpm to rad/sec is:
rad/sec = rpm × (2π) / 60
This works because one revolution equals 2π radians, and there are 60 seconds in a minute. By multiplying rpm (revolutions per minute) by 2π, you convert revolutions to radians. Dividing by 60 adjusts the time frame from minutes to seconds, resulting in radians per second.
For example, for 1500 rpm:
1500 × (2π) / 60 = 1500 × 6.2832 / 60 = 9424.8 / 60 ≈ 157.08 rad/sec.
Conversion Example
- Convert 1200 rpm to rad/sec:
- Multiply 1200 by 2π: 1200 × 6.2832 = 7539.84
- Divide by 60: 7539.84 / 60 = 125.66 rad/sec
- Convert 2000 rpm to rad/sec:
- 2000 × 6.2832 = 12566.4
- Divide by 60: 12566.4 / 60 = 209.44 rad/sec
- Convert 1000 rpm to rad/sec:
- 1000 × 6.2832 = 6283.2
- Divide by 60: 6283.2 / 60 = 104.72 rad/sec
Conversion Chart
| rpm | rad/sec |
|---|---|
| 1475.0 | 154.37 |
| 1480.0 | 154.98 |
| 1485.0 | 155.58 |
| 1490.0 | 156.19 |
| 1495.0 | 156.79 |
| 1500.0 | 157.08 |
| 1505.0 | 157.69 |
| 1510.0 | 158.29 |
| 1515.0 | 158.89 |
| 1520.0 | 159.50 |
| 1525.0 | 160.10 |
This chart helps you quickly find rad/sec values for rpm values in the range from 1475 to 1525. Read the rpm column, then look across to see the corresponding rad/sec for your needs.
Related Conversion Questions
- What is the rad/sec value for 1500 rpm?
- How many radians per second is 1500 rpm?
- Convert 1500 rpm to radians per second?
- What is the angular velocity in rad/sec for 1500 rpm?
- How do I convert 1500 rpm to radians per second?
- What is the rad/sec equivalent of 1500 rpm?
- Is 1500 rpm equal to how many radians per second?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in one minute, indicating rotational speed. It is used in engines, motors, and machinery to describe how fast something spins around an axis.
rad
Rad, short for radians, is a unit of angular measurement representing the angle created when the arc length equals the radius. One full circle equals 2π radians, making it a natural way to measure rotational angles in mathematics and physics.
Conversion FAQs
How can I quickly convert 1500 rpm to radians per second without a calculator?
Use the simplified formula: rad/sec = rpm × 0.1047. For 1500 rpm, multiply 1500 by 0.1047, resulting in approximately 157.05 rad/sec. This approximation helps make quick calculations easier without detailed math.
Why is the conversion factor 2π divided by 60 in the formula?
This factor accounts for converting revolutions, which are in units of 2π radians, per minute into radians per second. 2π converts revolutions to radians, and dividing by 60 changes minutes into seconds, standardizing the units.
Can this conversion be used for other rotational speeds besides rpm?
No, this specific formula applies only to rpm. To convert other units like degrees per second, different formulas are needed. For example, to convert degrees/sec to rad/sec, multiply degrees/sec by π/180.
What are some common applications of converting rpm to rad/sec?
This conversion is used in engineering, physics, and machinery to analyze rotational motion, calculate angular acceleration, torque, and power, or to synchronize rotating components in mechanical systems.
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