Test your understanding of centripetal force, its direction, and the real interactions that provide it. Apply the key formula to circular-motion examples and check your reasoning about common misconceptions.
Q1. What does the term centripetal force describe?
Centripetal force is the name for the inward net force responsible for the centripetal acceleration; it is not a separate kind of interaction.
Q2. Which equation gives the magnitude of the centripetal force for an object moving at speed ##v## in a circle of radius ##r##?
The centripetal-force magnitude is mass times speed squared divided by radius: ##F_c = \dfrac{mv^2}{r}##.
Q3. An object moves in a circle at constant speed. In which direction is its centripetal acceleration?
Centripetal acceleration points toward the centre, so the net force causing it also points toward the centre.
Q4. A ball is whirled in a horizontal circle on a string. What force supplies the inward centripetal force in this situation?
The string pulls the ball toward the centre, so its tension supplies the inward force needed for the circular motion.
Q5. What force supplies the centripetal force for a satellite moving in a circular orbit around a planet?
The planet's gravitational attraction acts toward the centre of the orbit and provides the satellite's centripetal force.
Q6. A car travels around a level, curved road without skidding. What force generally supplies the inward force needed to turn?
On a level road, friction between the tyres and the road can provide the inward force that turns the car.
Q7. Why is centripetal force not considered a separate fundamental interaction?
Centripetal force describes the inward net-force requirement. Tension, gravity, friction, or a normal force can provide it in particular situations.
Q8. A body moving in a circle has a net force directed toward the centre. What does Newton's second law imply about its acceleration?
Newton's second law makes the net force and acceleration point in the same direction. Thus an inward net force gives an inward acceleration.
Q9. If an object's speed doubles while its mass and circular-path radius stay unchanged, how does the required centripetal force change?
Since ##F_c = \dfrac{mv^2}{r}##, doubling ##v## multiplies ##v^2## by four, so the required force becomes four times as large.
Q10. A mass of ##2\ \text{kg}## moves at ##3\ \text{m/s}## in a circle of radius ##3\ \text{m}##. What is the centripetal-force magnitude?
Substitute into ##F_c = \dfrac{mv^2}{r}##: ##F_c = \dfrac{2(3^2)}{3} = 6\ \text{N}##.
Q11. An object moves at constant speed in a circle. Why can it still have acceleration?
Acceleration includes a change in velocity's direction as well as a change in speed. Circular motion changes direction continuously.
Q12. A car moves around a banked road. Which statement about the normal force is appropriate?
The normal force is perpendicular to the road surface. On a banked road, it can have an inward component that contributes to the required centripetal force.
Q13. Which choice correctly identifies the unit of force in the SI system?
Centripetal force is a force, so its SI unit is the newton.
Q14. An object of mass ##4\ \text{kg}## moves at ##2\ \text{m/s}## around a circle of radius ##2\ \text{m}##. What centripetal force is required?
Using ##F_c = \dfrac{mv^2}{r}## gives ##F_c = \dfrac{4(2^2)}{2} = 8\ \text{N}##.
Q15. A moving object has a centripetal-force requirement of ##20\ \text{N}##. If its mass and speed stay fixed while the radius doubles, what is the new required force?
For fixed mass and speed, ##F_c = \dfrac{mv^2}{r}## is inversely proportional to the radius. Doubling the radius halves the force, giving ##10\ \text{N}##.
Q16. A student says, “Centripetal force is an extra inward force added to tension, gravity, and friction.” What is the key error?
Centripetal force is not added as a new force in a free-body analysis. It describes the inward net force provided by actual interactions.
Q17. An object moves in a circular path. Which statement best describes the relationship between its net force and centripetal acceleration?
By Newton's second law, the net force and acceleration have the same direction. For circular motion, the centripetal components point toward the centre.
Q18. Which situation is best explained by gravity acting as the centripetal force?
A satellite in orbit is continually pulled toward its planet by gravity, which provides the inward force for its curved path.
Q19. For fixed mass and radius, which change would require the greatest increase in centripetal force?
The force depends on the square of speed. Changing from ##2## to ##4\ \text{m/s}## doubles the speed and therefore quadruples the force, the largest proportional increase among these choices.
Q20. A learner is identifying forces on a ball moving in a circle on a string. Which approach correctly determines the centripetal force?
The correct approach is to analyse the real forces and determine their net inward component. That net component is the centripetal force.