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(II) For each of the cases described below, sketch and label the total acceleration vector, the radial acceleration vector, and the tangential acceleration vector.
(c) A car slows down while rounding a curve of constant radius.
12. Rotational Kinematics
Types of Acceleration in Rotation
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A certain carnival ride is spinning, and smoothly changes its motion from clockwise to counterclockwise, stopping only for an instant in the middle. In this instant, which of the following is correct?
A
The radial acceleration is zero, and the tangential acceleration is also zero.
B
The radial acceleration is nonzero, but the tangential acceleration is zero.
C
The radial acceleration is nonzero, and the tangential acceleration is also nonzero.
D
The angular acceleration is zero, and the tangential acceleration is also zero.
E
The angular acceleration is zero, but the tangential acceleration is nonzero.
F
The radial acceleration is zero, but the tangential acceleration is nonzero.
Verified step by step guidance1
Understand the concept of radial and tangential acceleration: Radial acceleration is associated with the change in direction of velocity in circular motion, while tangential acceleration is associated with the change in the magnitude of velocity.
Identify the moment described in the problem: The ride is at an instant where it stops momentarily before changing direction from clockwise to counterclockwise.
Analyze radial acceleration: At the instant the ride stops, the velocity is zero, which means there is no change in direction of velocity. Therefore, the radial acceleration is zero.
Analyze tangential acceleration: Although the ride stops momentarily, it is changing its direction of motion, which implies a change in the magnitude of velocity. This indicates that there is a nonzero tangential acceleration.
Conclude the correct statement: Based on the analysis, the radial acceleration is zero because the velocity is momentarily zero, but the tangential acceleration is nonzero due to the change in the magnitude of velocity as the ride changes direction.
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