Questions: An object is undergoing circular motion with a tangential speed of 0.25 m / s. If the tangential speed were to double, how would this affect the centripetal acceleration? It would increase the centripetal acceleration by a factor of 4. It would not affect the centripetal acceleration. It would double the centripetal acceleration.

Solution Steps

Centripetal acceleration \( a_c \) for an object in circular motion is given by the formula:

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

where \( v \) is the tangential speed and \( r \) is the radius of the circular path.

If the tangential speed \( v \) is doubled, the new speed becomes \( 2v \). Substituting this into the formula for centripetal acceleration, we get:

\[ a_c' = \frac{(2v)^2}{r} = \frac{4v^2}{r} \]

The original centripetal acceleration is:

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

The new centripetal acceleration is:

\[ a_c' = \frac{4v^2}{r} \]

Comparing these, we see that:

\[ a_c' = 4a_c \]

This means the centripetal acceleration increases by a factor of 4.

Final Answer