Question 1

How to calculate centripetal force from mass, velocity, and radius?

Accepted Answer

To calculate centripetal force, square the linear tangential velocity (v), multiply by the object's mass (m), and divide by the radius of curvature (r): Fc = (m · v²) / r. For example, if a 1,200 kg car rounds a 50-meter radius curve at 20 m/s (72 km/h), the required centripetal force is (1,200 × 20²) / 50 = (1,200 × 400) / 50 = 9,600 Newtons (approx. 2,158 lbf).

Question 2

What is the difference between centripetal force and centrifugal force?

Accepted Answer

Centripetal force is a real inward force acting on a revolving body toward the center of curvature, observed from a stationary (inertial) reference frame. Centrifugal force is an apparent (fictitious or inertial) outward force experienced only from the rotating object's accelerating reference frame. When a car makes a sharp left turn, the friction pushing the tires inward is real centripetal force; the sensation of passengers being flung outward against the right door is centrifugal inertia resisting direction change.

Question 3

How do you calculate centripetal acceleration and g-force?

Accepted Answer

Centripetal acceleration is calculated using ac = v² / r (or ac = ω² · r when using angular speed in rad/s). To convert centripetal acceleration into G-force (the standard measure of lateral or radial loading), divide ac by Earth's standard gravitational acceleration (g0 = 9.80665 m/s² or 32.174 ft/s²). For instance, a go-kart rounding a 10-meter curve at 14 m/s generates ac = 14² / 10 = 19.6 m/s², which equals 19.6 / 9.80665 = 2.0g of lateral force.

Question 4

How does a banked turn prevent cars from skidding?

Accepted Answer

On a flat horizontal road, cars rely entirely on tire static friction to turn. When an engineer banks the road inward at an angle θ, the road surface normal force tilts inward. The horizontal vector component of this normal force (N · sin θ) points directly toward the center of the curve, providing centripetal force naturally. At the ideal design speed (where tan θ = v² / (g · r)), 100% of the centripetal force is provided by the road incline, allowing vehicles to traverse the turn safely even on slick ice with zero tire friction.

Question 5

What is the minimum critical velocity required to stay on a vertical loop?

Accepted Answer

The minimum speed required at the top apex of a vertical circular loop is vcrit = √(g · r), where g is gravitational acceleration (9.81 m/s²) and r is loop radius. At this precise velocity, gravity alone provides 100% of the required centripetal acceleration, meaning the normal force against the track is zero (0G weightlessness). If velocity drops below √(g · r), centripetal acceleration is insufficient to maintain the circular arc, and the object detaches or falls out in a parabolic trajectory.

Question 6

How do you convert centrifuge RPM to RCF (g-force)?

Accepted Answer

To convert centrifuge revolutions per minute (RPM) to Relative Centrifugal Force (RCF in multiples of g), use the standard equation: RCF = 1.118 × 10⁻⁵ × r(cm) × RPM², where r(cm) is the rotor radius in centimeters. For example, spinning a rotor with an 8.5 cm radius at 10,000 RPM produces RCF = 1.118 × 10⁻⁵ × 8.5 × (10,000)² = 9,503 x g.

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