For an object spinning around a central point, what will happen if its distance from the center is decreased?

Question

Nothing will change.

O The centripetal force will decrease.

O Its acceleration will increase.

Its acceleration will decrease.

Answer 1

For an object spinning around a central point, if its distance from the center is decreased, the correct answer is:

O Its acceleration will increase.

Here's the reasoning: The centripetal acceleration of an object moving in a circular path is given by the formula:

\[ a_c = \frac{v^2}{r} \]

where \( a_c \) is the centripetal acceleration, \( v \) is the linear velocity, and \( r \) is the distance from the center.

If the distance \( r \) decreases while keeping the speed \( v \) constant, the value of \( \frac{v^2}{r} \) increases, leading to an increase in centripetal acceleration. Additionally, if the object is being spun faster due to the decrease in radius (like a figure skater pulling in their arms), the acceleration would also increase. Therefore, reducing the distance from the center increases the centripetal acceleration.