# 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*

*a _{tan}* = tangential acceleration

*r* = radius of the object's rotation

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

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*

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

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

The tangential acceleration of the tires is 2.40 m/s^{2} (this is also the resulting acceleration of the car).

2) A child spins a toy top, applying a force to the peg in the middle. The force applied results in a tangential acceleration of the peg. If the radius of the peg is 0.50 cm (0.0050 m), and the tangential acceleration applied is a_{tan} = 0.540 m/s^{2}, what is the angular acceleration of the top?

Answer: The angular acceleration can be found by rearranging the equation:

α =

α = 108 radians/s^{2}

The angular acceleration of the top is 108 radians/s^{2}.

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