## Tangential Acceleration Formula

#### In rotational motion, tangential acceleration is a measure of how quickly a tangential velocity changes. It always acts perpendicular to the centripetal acceleration of a rotating object. It is equal to the angular acceleration α, times the radius of the rotation.

*tangential acceleration = (radius of the rotation)(angular acceleration)*

*a*_{tan} = rα

_{tan}= rα

*a*_{tan} = tangential acceleration

_{tan}

*r* = radius of the object’s rotation

*α* = angular acceleration, with units radians/s^{2}

####
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**Tangential Acceleration Formula Questions:**

#### 1) A car that has tires with radius 20.0 cm (0.200 m) begins to accelerate forward. The acceleration comes from the engine, which produces an angular acceleration of the tires α = 12.0 radians/s^{2}. What is the tangential acceleration of the tires?

**Answer:** The tangential acceleration of the tires can be found from the formula:

*a*_{tan} = rα

_{tan}= rα

*a*_{tan} = (0.200 m)(12.0 radians/s^{2})

_{tan}= (0.200 m)(12.0 radians/s

^{2})

*a*_{tan} = 2.40 m/s^{2}

_{tan}= 2.40 m/s

^{2}