What is the centripetal force of an object undergoing uniform circular motion when its radius is doubled and its speed remains constant?
F₁=mv²/R₁
F₂=mv²/R₂=mv²/2R₁=F₁/2
half as great as before
To determine the centripetal force of an object undergoing uniform circular motion, you need to use the formula:
F = (m * v^2) / r
where:
- F is the centripetal force
- m is the mass of the object
- v is the velocity of the object
- r is the radius of the circular path taken by the object.
In this case, you are asked to calculate the centripetal force when the radius is doubled while the speed remains constant. Since the speed remains constant, the velocity (v) does not change.
To find out how the centripetal force changes when the radius is doubled, we need to substitute the new radius into the formula and compare it with the original scenario.
Let's assume:
- F1 is the original centripetal force
- r1 is the original radius
- r2 is the new radius (which is double the original radius)
With this in mind, the equation becomes:
F2 = (m * v^2) / (2 * r1)
Here, we see that when the radius doubles, the centripetal force is divided by 2.
So, the centripetal force of an object undergoing uniform circular motion, where its radius is doubled and its speed remains constant, will be half of its original value.