A body is moving in a circle with a speed of 1m/s. This speed increases at the rate of
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The acceleration of an object is a description of how its velocity is changing as time goes by. It’s actually more complex than it sounds since we have a lot of preconceived notions about motion that are incomplete or sometimes, dead wrong.
To better understand acceleration, I tell my students to imagine a tiny string attached to the object. Then, imagine which way the string would have to pull to change the motion of the object in the way you observe.
For objects moving in a circle, their speed around the circle (tangental speed) does not need to change. The direction they are traveling in certainly does change (the vector nature of velocity makes direction equally important as the magnitude, or speed) Because the direction is changing, then the velocity must be changing and a changing velocity is acceleration.
The direction of the acceleration can be imagined by using the string concept I mentioned above. A string would have to pull toward the center in order to bend the object’s path into a circle shape. (if you swing a weight on a string, then you will find that you actually do pull on the string toward your hand) This acceleration toward the center of a circle is called centripetal acceleration.
The amount or magnitude of the acceleration can be determined by squaring the magnitude of the velocity (i.e. the speed) and dividing it by the radius of the circular path the object moves in.
In your example, the speed is 1 meter in one second or 1 m/s. You did not mention the radius of the circle which is critical to finish the calculation. 1 m/s divided by the radius is the magnitude of the acceleration. The direction is toward the center of the circle.
To better understand acceleration, I tell my students to imagine a tiny string attached to the object. Then, imagine which way the string would have to pull to change the motion of the object in the way you observe.
For objects moving in a circle, their speed around the circle (tangental speed) does not need to change. The direction they are traveling in certainly does change (the vector nature of velocity makes direction equally important as the magnitude, or speed) Because the direction is changing, then the velocity must be changing and a changing velocity is acceleration.
The direction of the acceleration can be imagined by using the string concept I mentioned above. A string would have to pull toward the center in order to bend the object’s path into a circle shape. (if you swing a weight on a string, then you will find that you actually do pull on the string toward your hand) This acceleration toward the center of a circle is called centripetal acceleration.
The amount or magnitude of the acceleration can be determined by squaring the magnitude of the velocity (i.e. the speed) and dividing it by the radius of the circular path the object moves in.
In your example, the speed is 1 meter in one second or 1 m/s. You did not mention the radius of the circle which is critical to finish the calculation. 1 m/s divided by the radius is the magnitude of the acceleration. The direction is toward the center of the circle.
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