Tangential Acceleration Formula

The tangential acceleration is denoted by the symbol a_t. Its unit of measurement is the same as linear acceleration, that is, meters per square second (m/s²). Its dimensional formula is given by [M⁰L¹T^-2]. Its formula is given by the product of the radius of a circular path and the angular acceleration of the rotating object.

a_t = r α

where,

• a_t is the tangential acceleration,
• r is the radius of circular path,
• α is the angular acceleration.

The above expression gives the relation between tangential acceleration and angular acceleration.

Now, in terms of angular velocity and time, the formula is given by,

a_t = r (ω/t)

where,

• a_t is the tangential acceleration,
• ω is the angular velocity,
• t is the time taken.

In terms of angular displacement and time, the formula is given by,

a_t = r (θ/t²)

where,

• a_t is the tangential acceleration,
• θ is the angular displacement or angle of rotation,
• t is the time taken.

Following are the various cases possible for different values of Tangential Acceleration:

1. When a_t is greater than Zero: The object has an accelerated motion, and the magnitude of velocity will increase with time.
2. When a_t is Less than Zero: The object has a deaccelerated or slow motion, and the magnitude of velocity will decrease with time.
3. When a_t is Equal to Zero: The object has a uniform motion, and the magnitude of velocity will remain constant.

Read More: Uniformly Accelerated Motion

Tangential acceleration is the rate at which a tangential velocity varies in the rotational motion of any object. It acts in the direction of a tangent at the point of motion for an object. The tangential velocity also acts in the same direction for an object undergoing circular motion. Tangential acceleration only exists when an object travels in a circular path. It is positive if the body is rotating at a faster velocity, negative when the body is decelerating, and zero when the body is moving uniformly in the orbit.