A small sphere is swung in a vertical circle. Which of the following combinations represents the direction of the velocity and acceleration at the right-most point of the cirlce?
Question
A small sphere is swung in a vertical circle. Which of the following combinations represents the direction of the velocity and acceleration at the right-most point of the cirlce?
Solution
The direction of the velocity and acceleration at the right-most point of the circle would be as follows:
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Velocity: The direction of the velocity of an object moving in a circle is always tangential to the circle. This means it is perpendicular to the radius at any given point. So, at the right-most point of the circle, the velocity would be directed straight down.
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Acceleration: There are two components of acceleration in circular motion - radial (or centripetal) acceleration and tangential acceleration. The radial acceleration is always directed towards the center of the circle. So, at the right-most point of the circle, the radial acceleration would be directed to the left. The tangential acceleration depends on whether the speed of the object is changing. If the speed is constant, there is no tangential acceleration. If the speed is increasing, the tangential acceleration is in the same direction as the velocity. If the speed is decreasing, the tangential acceleration is in the opposite direction of the velocity.
So, without more information about the speed of the sphere, we can't definitively say the direction of the total acceleration. But we can say that one component of the acceleration (the radial acceleration) is directed to the left.
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