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Tangential Acceleration Calculator

Find the linear acceleration at a point on a rotating body given its radius and angular acceleration.

How it is calculated

The tool multiplies the distance from the axis by the angular acceleration: at = r × α. Here r is the radius in metres, α is the angular acceleration in rad/s², and at comes out in m/s², rounded to two decimals. The radius cannot be negative, so a negative radius gives no result. The angular acceleration may be negative: that simply means the body is slowing down, and the answer takes the same sign. A radius of zero gives 0.00 m/s², because a point on the axis does not move along a circle. Only the along-the-path component is computed; the inward centripetal part (r × ω²) is not included.

Worked example

A flywheel has a radius of 0.35 m and speeds up at 6 rad/s². Step 1: r = 0.35 m. Step 2: α = 6 rad/s². Step 3: multiply, 0.35 × 6 = 2.1. The tool prints 2.10 m/s²: the point on the rim gains speed along its path at that rate.

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Common mistakes

  • Entering the diameter instead of the radius, which doubles the answer.
  • Typing the angular acceleration in rpm per second or degrees per second squared instead of rad/s².
  • Entering angular velocity (rad/s) in the angular acceleration field; that quantity gives the centripetal acceleration, not the tangential one.
  • Typing a negative radius to show direction. Use a positive radius and put the sign on the angular acceleration if the body is slowing.

About this calculator

Tangential acceleration is the component of a rotating point's linear acceleration that acts along the direction of motion, tangent to its circular path, and it is what changes the point's speed as it moves, as opposed to centripetal acceleration, which points toward the center and only changes direction. It is calculated from the radius of the circular path and the angular acceleration with the formula a_t = r × α, where α is in radians per second squared.

Engineers use tangential acceleration to analyze anything that speeds up or slows down while rotating — a flywheel spinning up under motor torque, a gear tooth engaging under load, a centrifuge ramping to speed, or a point on a car wheel accelerating from a stop — since the total linear acceleration of that point is the vector sum of this tangential component and the centripetal component (a_c = r × ω²).

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