When an object moves along a curved path, the instantaneous acceleration can be broken into two components: one perpendicular to the curve (the centripetal acceleration) and one tangent to the curve (the tangential acceleration).
Definition11.4.1.Tangential Acceleration.
The tangential acceleration of an object, \(a_t\text{,}\) points parallel to the instantaneous velocity, in the same direction if the object is speeding up and in the opposite direction if the object is slowing down.
ExercisesCentripetal and Tangential Acceleration
Recall the Curved Road Figure, which shows a car moving counterclockwise while slowing down.
1.
Indicate the direction of the centripetal acceleration of the car.
2.
Indicate the direction of the tangential acceleration of the car.
3.
Draw a vector for the instantaneous acceleration of the car. How did you use the previous answers?
Answer.
The figure shows that the tangential and centripetal accelerations are components of the instantaneous acceleration. They can be added together to create the combined instantatenous acceleration vector.
Figure11.4.2.Acceleration vectors for a car moving along a curved road.
4.
Suppose the speed of the car decreases at a constant rate as it moves around the track. How does each acceleration (centripetal, tangential, and the combined instantaneous) change?
Answer.
Since the speed is decreasing at a constant rate, the tangential acceleration will be constant. However, the centripetal acceleration depends on the speed, so it will decrease as the car slows down. Since one component is constant and the other is decreasing, the magnitude of the instantaneous accleration will also decrease.
5.
Consider the Models Steps. How would you answer them after what you have learned so far?
