1500 RPM to Rad – Answer with Formula

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1500 rpm equals approximately 157.08 radians per second.

This is because to convert revolutions per minute (rpm) to radians per second (rad/sec), you multiply the rpm value by 2π (approximately 6.2832) and then divide by 60, since there are 2π radians in one revolution and 60 seconds in a minute.

Conversion of 1500 rpm to radians per second

To convert 1500 rpm into radians per second, we use the conversion formula: rad/sec = rpm × 2π / 60. Plugging in 1500 rpm: rad/sec = 1500 × 6.2832 / 60 = 1500 × 0.10472 ≈ 157.08 rad/sec. This process involves translating revolutions into radians and minutes into seconds to get the angular velocity.

Conversion Tool

Conversion Formula

The formula to convert rpm to rad/sec is rad/sec = rpm × 2π / 60. This works because each revolution contains 2π radians, and there are 60 seconds in a minute, so multiplying rpm by 2π gives radians per minute, dividing by 60 converts it to radians per second. For example, 1500 rpm: 1500 × 2π / 60 = 1500 × 0.10472 ≈ 157.08 rad/sec.

Conversion Example

• Convert 1000 rpm to rad/sec:
  • Step 1: Multiply 1000 by 2π: 1000 × 6.2832 = 6283.2 radians per minute.
  • Step 2: Divide by 60: 6283.2 / 60 ≈ 104.72 rad/sec.
• Convert 2000 rpm to rad/sec:
  • Step 1: 2000 × 6.2832 = 12566.4 radians per minute.
  • Step 2: 12566.4 / 60 ≈ 209.44 rad/sec.
• Convert 750 rpm to rad/sec:
  • Step 1: 750 × 6.2832 = 4719.6 radians per minute.
  • Step 2: 4719.6 / 60 ≈ 78.66 rad/sec.
• Convert 1800 rpm to rad/sec:
  • Step 1: 1800 × 6.2832 = 11309.76 radians per minute.
  • Step 2: 11309.76 / 60 ≈ 188.50 rad/sec.
• Convert 2500 rpm to rad/sec:
  • Step 1: 2500 × 6.2832 = 15708 radians per minute.
  • Step 2: 15708 / 60 ≈ 261.80 rad/sec.

Conversion Chart

This chart helps you find the rad/sec conversions for rpm values between 1475 and 1525. Just cross-reference your rpm value with the corresponding rad/sec value to quickly get the answer.

Related Conversion Questions

• How many radians per second are in 1500 rpm?
• What is the rad/sec equivalent of 1500 revolutions per minute?
• Convert 1500 rpm to radians per second with detailed steps?
• How do I calculate radians per second from rpm for 1500 rpm?
• What is the angular velocity in rad/sec for 1500 rpm?
• Is 1500 rpm equal to approximately 157 radians per second?
• How do I convert a motor speed of 1500 rpm into radians per second?

Conversion Definitions

rpm

Revolutions per minute (rpm) measures how many complete turns an object makes in one minute. It is a rotational speed unit used in engines, motors, and machinery to describe how fast a shaft or wheel spins.

rad

Rad, short for radians, measure angles based on the radius of a circle. One radian is the angle where the arc length equals the radius, and there are 2π radians in a full circle, providing a natural unit for angular measurement in mathematics and physics.

Conversion FAQs

How accurate is the conversion from rpm to rad/sec?

The conversion is highly accurate when you use the exact formula rad/sec = rpm × 2π / 60. Minor inaccuracies may occur due to rounding π or the calculator’s decimal precision, but generally, the results are precise enough for engineering purposes.

Can I convert rad/sec back to rpm using the same formula?

Yes, reversing the process involves multiplying rad/sec by 60 and dividing by 2π: rpm = rad/sec × 60 / 2π. This allows you to switch between units based on what measurement is needed for your application.

What is the significance of converting rpm to rad/sec?

Converting rpm to rad/sec is vital when dealing with angular velocity in physics or engineering, as rad/sec is the standard unit in many formulas involving rotational motion, torque, and angular acceleration, making calculations more consistent and universal.