Angular versus Centripetal Acceleration
Date: Fall 2013
How can an object move with an angular acceleration=0 but have a non-zero value for centripetal acceleration?
Angular acceleration is a measure of the rate of change of rotating speed. If something is moving in a circle without changing its speed of rotation around the center, then angular acceleration around the center is zero. Angular acceleration is measured in radians per second-squared (rad/s^2) or in revolutions per second-squared (rev/s^2).
Centripetal acceleration is a measure of how tightly an object changes direction. When an object quickly turns a sharp corner, centripetal acceleration is huge. When an object slowly and passes through a wide turn, centripetal acceleration is very small. When an object travels in a circle, that object is always changing direction, always turning. There is always centripetal acceleration. Centripetal acceleration is measured in meters per second-squared (m/s^2).
Dr. Ken Mellendorf
Thank you for your question. I think I understand the issue here:
Velocity includes both speed and direction. If an object is in space and has no force applied to it, its speed, direction, and velocity will all remain constant.
Acceleration (in general) refers any change in velocity. In order to have acceleration, you need to apply force according to Force = Mass x Acceleration.
If you swing a tethered ball around in a circle at a fixed rate, it will have a constant speed and constant angular velocity. Angular velocity is (degrees or radians) per second. That will be constant because the ball is orbiting at a fixed rate. However, because it's direction is always changing it will be always accelerating. This is centripetal acceleration. The tether transmits the force which is required for the centripetal acceleration. (We are ignoring the drag of air resistance and drag from other factors.)
When you are in a car traveling rapidly around a curve, your body tends to lean against the side of the car that is on the outside of the curve. In fact, what is happening is that the car is accelerating your mass towards the inside of the curve. This is another example of centripetal acceleration which can happen without angular acceleration. Acceleration can mean ANY change in velocity. This can be direction OR speed (or both.)
I hope this helps.
In considering this as a vector problem, as a point travels around on the circumference of a circle at a constant speed, 0 angular acceleration, the velocity vector is changing direction and therefore exhibits a non-zero value.
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