Acceleration in terms of velocity and radius?

In summary, the question is asking which of the given quantities has dimensions of [(ML)/(T^2)]. To solve this, we can use the basic dimensions of mass (M), time (T), and length (L). From the options, we can see that each quantity includes mass (M), so we need to determine the combination of velocity (V) and radius (R) that gives us dimensions of acceleration. Since acceleration is defined as [(ML)/(T^2)], we can see that V^2/R gives us the correct dimensions. Therefore, the correct answer is MV^2/R.
  • #1
winbacker
13
0
Acceleration in terms of velocity and radius??!

Homework Statement



Which one of the quantities below has dimensions = [(ML)/(T^2)]

MV
MV^2
(MV^2)/R
MRV
(MV^2)/(R^2)



Homework Equations



My physics textbook defines 3 basic dimesions: M = Mass. T = Time. L = Length.



The Attempt at a Solution



I know that [(ML)/(T^2)] = mass x acceleration. Each of the 5 possible answers has an "M" which is mass. Therefore, I'm assuming that acceleration must be expressed in terms of
"R" (which I think might be radius) and V (which I think is velocity).

Is this line of thinking correct? As in, can acceleration be expressed in terms of Velocity and Radius? Or is this line of thinking way off the mark?
 
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  • #2


What re the units of velocity. What units is the radius expressed in? Once you know that, try looking at which of the options units combine to give you what you want.
 
  • #3




Yes, your line of thinking is correct. Acceleration can be expressed in terms of velocity and radius. In fact, the equation for centripetal acceleration is given by a = v^2/r, where v is the velocity and r is the radius of the circular motion. Therefore, the correct answer would be (MV^2)/R, as it has dimensions of [(ML)/(T^2)].
 

1. What is the formula for acceleration in terms of velocity and radius?

The formula for acceleration in terms of velocity and radius is a = v²/r, where a is acceleration, v is velocity, and r is the radius.

2. How does acceleration affect velocity in circular motion?

Acceleration affects velocity in circular motion by changing its direction. As an object moves in a circular path, its velocity constantly changes due to the change in direction. This change in velocity is caused by the acceleration towards the center of the circle.

3. Can acceleration and velocity be in opposite directions?

Yes, acceleration and velocity can be in opposite directions. In circular motion, the velocity is tangent to the circle and the acceleration is towards the center of the circle. This means that the direction of the acceleration is perpendicular to the direction of the velocity, resulting in them being in opposite directions.

4. How do radius and velocity affect acceleration?

Radius and velocity directly affect acceleration. A smaller radius or a larger velocity will result in a greater acceleration. This is because a smaller radius means the object is moving in a tighter circle, and a larger velocity means the object is moving faster, resulting in a higher acceleration towards the center of the circle.

5. What is centripetal acceleration?

Centripetal acceleration is the acceleration towards the center of a circular path. It is caused by the change in direction of an object in circular motion and is always perpendicular to the velocity. It is calculated using the formula a = v²/r, where a is the centripetal acceleration, v is the velocity, and r is the radius.

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