If a block of mass moves in a circle of radius r at constant speed v on a horizontal frictionless table, which forces must provide the centripetal acceleration?

If a block of mass moves in a circle of radius r at constant speed v on a horizontal frictionless table, which forces must provide the centripetal acceleration?

• A. The tangential component of velocity provides the centripetal acceleration
• B. The net inward force toward the center provides the centripetal acceleration
• C. The gravitational force provides the centripetal acceleration
• D. The outward normal force provides the centripetal acceleration

Answer: (B)

Centripetal acceleration comes from the net force directed toward the center of the circle. It isn’t caused by velocity itself; velocity merely indicates the direction the object is moving. Here, gravity and the normal force cancel each other vertically, so they don’t provide any horizontal inward push. The inward force must come from the constraint that keeps the block circling the center—such as tension in a string or a central track reaction—which together furnish the net inward force equal to m v^2 / r. Therefore, the centripetal acceleration is provided by the net inward force toward the center.

Centripetal acceleration comes from the net force directed toward the center of the circle. It isn’t caused by velocity itself; velocity merely indicates the direction the object is moving. Here, gravity and the normal force cancel each other vertically, so they don’t provide any horizontal inward push. The inward force must come from the constraint that keeps the block circling the center—such as tension in a string or a central track reaction—which together furnish the net inward force equal to m v^2 / r. Therefore, the centripetal acceleration is provided by the net inward force toward the center.