Lesson 8 - Circular Motion

What is the direction of centripetal force acting on an object moving in a circle?

• Tangential to the circle
• Radially outward from the center
• Radially inward towards the center
• Perpendicular to the plane of motion

Answer explanation

The centripetal force always acts radially inward, towards the center of the circle, keeping the object in circular motion.

A skateboarder is riding in a perfect circle in an empty parking lot at a constant speed. Which of the following statements about the skateboarder's motion is true?

• The skateboarder has zero acceleration.
• The skateboarder's velocity is constant.
• The skateboarder's speed is changing.
• The skateboarder is accelerating towards the center of the circle.

Answer explanation

Even at constant speed, the direction of velocity changes, so the skateboarder is accelerating towards the center (centripetal acceleration).

A model airplane flies in a horizontal circle at the end of a 1.5-meter string. If the airplane completes 10 revolutions in 20 seconds, what is its speed?

• 0.75 m/s
• 1.5 m/s
• 4.71 m/s
• 9.42 m/s

Answer explanation

Speed = distance/time = (10 × 2π × 1.5 m) / 20 s ≈ 4.71 m/s.

Two identical cars, Car A and Car B, are driving around separate circular tracks. Car A is on a track with twice the radius of Car B's track, but both cars maintain the same tangential speed. How does the centripetal force required for Car A compare to Car B?

• Car A requires twice the centripetal force.
• Car A requires half the centripetal force.
• Car A requires four times the centripetal force.
• Car A requires one-fourth the centripetal force.

Answer explanation

Centripetal force is inversely proportional to radius for constant speed: F_c = mv^2/r. Doubling the radius halves the force.

A theme park designer is evaluating the safety of a new ride that spins passengers in a horizontal circle. The ride uses a fixed radius, but the rotational speed can vary. To maximize the thrill while ensuring passenger safety, which of the following rotational speed adjustments would be the most critical to avoid excessive centripetal forces on riders?

• Keeping the speed constant throughout the ride.
• Gradually increasing the speed during the ride.
• Limiting the maximum speed the ride can achieve.
• Rapidly decreasing the speed at the end of the ride.

Answer explanation

Centripetal force increases with the square of speed, so limiting the maximum speed is most critical for safety.

As a hacker, you've gained access to the control system of a facility's uranium enrichment centrifuges. To ensure their destruction, you need to spin them beyond their structural limits. Each centrifuge has an effective arm length (radius) of 0.8 meters, and they are designed to break if the centripetal acceleration exceeds 5.0 × 10⁵ m/s². At what minimum speed, in meters per second, must you command the centrifuges to spin to achieve this critical acceleration and cause them to fail?

• 200 m/s
• 400 m/s
• 632 m/s
• 894 m/s

Answer explanation

Use a_c = v^2/r ⇒ v = sqrt(a_c × r) = sqrt(5.0 × 10^5 × 0.8) ≈ 632 m/s.