Direction of centrifugal (inertial) force in circular motion For a mass m moving in a circular path of radius r with speed v (or angular speed ω), the centrifugal force acts in which direction?

Introduction / Context:
In circular motion analysis, two viewpoints exist: an inertial (laboratory) frame and a rotating (body-attached) frame. The real required force is centripetal (toward the center). In the rotating frame, an equal and opposite inertial (fictitious) force called centrifugal appears to act on the mass.

Given Data / Assumptions:

• Uniform circular motion with radius r and speed v (or angular speed ω).
• Rotating-frame interpretation for centrifugal force.
• Rigid, frictionless idealization where applicable.

Concept / Approach:

Centripetal requirement: a_c = v^2 / r = ω^2 r directed toward the center. In a rotating frame, this is balanced by the inertial (centrifugal) force of magnitude m v^2 / r = m ω^2 r directed radially outward, away from the center.

Step-by-Step Solution:

Verification / Alternative check:

Free-body diagram in rotating frame: inward real forces are balanced by outward centrifugal force, giving apparent equilibrium for steady rotation.

Why Other Options Are Wrong:

(a) Tangential direction corresponds to tangential acceleration when speed changes. (b) Describes centripetal, not centrifugal. (d) and (e) are incorrect for nonzero circular motion.

Common Pitfalls:

Confusing centripetal with centrifugal; forgetting that centrifugal is a fictitious force used only in non-inertial frames.

Final Answer:

Away from the center of rotation