Questions: Which formula can be used to find the centripetal acceleration of an orbiting object? ac = sqrt(v)/T ac = v^2/T ac = v^2/r ac = sqrt(v)/r

Which formula can be used to find the centripetal acceleration of an orbiting object?
ac = sqrt(v)/T
ac = v^2/T
ac = v^2/r
ac = sqrt(v)/r
Transcript text: Which formula can be used to find the centripetal acceleration of an orbiting object? $a_{c}=\frac{\sqrt{v}}{T}$ $a_{c}=\frac{v^{2}}{T}$ $a_{c}=\frac{v^{2}}{r}$ $a_{c}=\frac{\sqrt{v}}{r}$
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Solution

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Solution Steps

Step 1: Understanding Centripetal Acceleration

Centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed towards the center of the circle. The formula for centripetal acceleration is derived from the relationship between velocity, radius, and acceleration in circular motion.

Step 2: Analyzing the Given Options

We are given four options for the formula of centripetal acceleration:

  1. ac=vT a_{c} = \frac{\sqrt{v}}{T}
  2. ac=v2T a_{c} = \frac{v^{2}}{T}
  3. ac=v2r a_{c} = \frac{v^{2}}{r}
  4. ac=vr a_{c} = \frac{\sqrt{v}}{r}
Step 3: Identifying the Correct Formula

The correct formula for centripetal acceleration is:

ac=v2r a_{c} = \frac{v^{2}}{r}

where v v is the tangential velocity of the object and r r is the radius of the circular path.

Final Answer

The correct formula for centripetal acceleration is ac=v2r\boxed{a_{c} = \frac{v^{2}}{r}}.

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