The tangential acceleration of a point on a rotating object equals the distance of that point from the axis of rotation multiplied by the angular acceleration direction of rotation angular momentum tangential speed radius
The Correct Answer and Explanation is:
Correct answer:
Angular acceleration
Explanation:
Tangential acceleration refers to the linear acceleration of a point on a rotating object, measured along the path of rotation. It describes how quickly the speed of the object is changing in the tangential (circular) direction. The formula for tangential acceleration is: at=r⋅αa_t = r \cdot \alphaat=r⋅α
Where:
- ata_tat is the tangential acceleration,
- rrr is the distance from the axis of rotation (also called the radius),
- α\alphaα is the angular acceleration.
This formula shows that tangential acceleration is directly proportional to both the radius and the angular acceleration. This means that if either the distance from the center or the angular acceleration increases, the tangential acceleration increases as well.
Why angular acceleration is the correct answer:
Angular acceleration refers to how quickly the rotational speed of an object is changing. It is the rotational counterpart of linear acceleration. The further a point is from the axis (larger radius), the greater its tangential acceleration will be, provided the object is experiencing angular acceleration.
Let us briefly evaluate the other options:
- Direction of rotation: This determines the orientation (clockwise or counterclockwise) but does not determine the amount of tangential acceleration.
- Angular momentum: This is a measure of rotational motion, depending on the moment of inertia and angular velocity, but it is not part of the formula for tangential acceleration.
- Tangential speed: This is related to how fast a point is moving along a circular path, but it does not involve acceleration unless its value is changing.
- Radius: While it is part of the formula, it is not the quantity that must be multiplied to determine the tangential acceleration — it is the angular acceleration that gets multiplied by radius.
Thus, angular acceleration is the correct answer.
