Understanding Acceleration: A Simple Test Question

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In summary, the ball is not accelerating because it is always moving forward, even though it is traveling in a circular path.
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Lord Patrick
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I have a very simple test question about acceleration. A ball is moving at a constant speed inside of a hollow sphere. The question is whether or not the ball is accelerating. I said that it was not accelerating because the ball is always moving forward, even though it is traveling in a circular path. My teacher said that it was accelerating but the only explanation that I was given was that the ball is moving in a circle. This is a very simple question, but it is bothering the heck out of me.
 
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  • #2
What is the definition of acceleration?

What is the difference between speed and velocity?
 
  • #3
Lord Patrick said:
I have a very simple test question about acceleration. A ball is moving at a constant speed inside of a hollow sphere. The question is whether or not the ball is accelerating. I said that it was not accelerating because the ball is always moving forward, even though it is traveling in a circular path. My teacher said that it was accelerating but the only explanation that I was given was that the ball is moving in a circle. This is a very simple question, but it is bothering the heck out of me.
If a ball with a mass m makes a circular motion, the direction of the velocity is constantly changing. In order to change the velocity of an object, a force is needed, and F=ma. If there were no acceleration, the ball wouldn't go in a circle, but simply in a straight line.

The acceleration we're talking about when some object goes in a circle is the centripetal acceleration. So you could say that the ball is accelerated to the center by the centripetal force.
 
  • #4
Are you taking about a moving ball inside a stationary hollow sphere (in an inertial coordinate system)? Are you talking about a ball with a constant speed (a scalar) and not a constant velocity (a vector)? Is the ball rolling without slipping on the inside surface of the hollow sphere? Is the ball rolling without slipping on the inside surface of the sphere under the influence of gravity? Is the ball solid, with uniform density? Are you talking about the ball rolling in a horizontal plane only (no vertical motion)?
 
  • #5
Welcome to PF!

Hi Lord Patrick! Welcome to PF! :smile:
Lord Patrick said:
… I said that it was not accelerating because the ball is always moving forward, even though it is traveling in a circular path.

Anything whose velocity is changing is accelerating …

so is its velocity changing? :wink:
 

1. What is acceleration?

Acceleration is the rate of change of velocity over time. It is a measure of how quickly the velocity of an object is changing. In simpler terms, it is the speed at which an object is speeding up or slowing down.

2. How is acceleration calculated?

Acceleration is calculated by dividing the change in velocity by the change in time. The formula for acceleration is a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. What are the units of acceleration?

The units of acceleration depend on the units of velocity and time used in the calculation. For example, if velocity is measured in meters per second (m/s) and time is measured in seconds (s), then the units of acceleration would be meters per second squared (m/s^2).

4. How does acceleration differ from velocity?

Velocity is a measure of an object's speed and direction, while acceleration is a measure of how an object's velocity is changing. Velocity tells us how fast an object is moving, while acceleration tells us how quickly its speed is changing.

5. What factors affect acceleration?

The factors that affect acceleration include the force applied to the object, the mass of the object, and the direction of the force relative to the direction of motion. A larger force or a smaller mass will result in a greater acceleration. Additionally, if the force is in the same direction as the motion, the acceleration will be positive, while a force in the opposite direction will result in a negative acceleration (deceleration).

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