Circular Motion Dynamics - UNSOLVED PRACTICE SET

Q7. Define centripetal force. Why is it called a "real" force? Who provides this force in the case of:

(a) A satellite orbiting the Earth

(b) A car taking a turn on a level road

Q8. Explain why a cyclist leans inward while taking a turn. Draw a diagram showing the forces.

Q9. A 500 kg car takes a turn of radius 50 m at 36 km/h. Calculate the centripetal force required. What provides this force?

Q10. In a circus "death well" of radius 15 m, what is the minimum speed a motorcyclist must have at the top to avoid falling? (Take g = 10 m/s²)

Q11. Distinguish between centripetal force and centrifugal force. Why is centrifugal force called a "pseudo force"?

Q12. A stone tied to a string is whirled in a vertical circle of radius 1 m. Calculate the minimum speed required at the lowest point to complete the circle. (Take g = 10 m/s²)

Q13. Explain the dynamics of uniform circular motion. Derive the expression for centripetal force. Discuss how this force is provided in the following cases:

(i) A stone whirled at the end of a string

(ii) A vehicle on a level circular road

(iii) A vehicle on a banked road

(iv) An electron revolving around the nucleus

Include free body diagrams for (ii) and (iii).

Q14. A car of mass 1000 kg moves on a flat circular track of radius 100 m.

(a) If the coefficient of friction is 0.5, calculate the maximum speed without skidding.

(b) If the track is banked at 30°, calculate the ideal speed for no friction.

(c) If the car moves at 30 m/s on the banked track, calculate the frictional force required (μ = 0.2).

(d) What happens if the car's speed exceeds the maximum safe speed?

Q15. A small block of mass m is placed on a rotating turntable at a distance r from the centre. The coefficient of static friction is μ.

(a) Draw the free body diagram.

(b) Derive the expression for the maximum angular velocity before the block starts sliding.

(c) If m = 0.1 kg, r = 0.2 m, and μ = 0.4, calculate this maximum angular velocity.

(d) What happens if the turntable's speed is increased beyond this value?

(e) How does the position of the block affect its tendency to slide?

Q16. A 70 kg pilot is flying a jet in a vertical loop of radius 500 m at a constant speed of 200 m/s.

(a) Calculate the force exerted by the seat on the pilot at the bottom of the loop.

(b) Calculate the force exerted by the seat on the pilot at the top of the loop.

(c) Calculate the minimum speed required at the top for the pilot to remain in contact with the seat.

(d) Explain why the pilot feels "heavier" at the bottom and "lighter" at the top.

(e) What is the apparent weight of the pilot at the bottom? (Take g = 10 m/s²)

Q17. A train rounds a bend of radius 800 m at 72 km/h. The distance between the rails is 1.5 m. The outer rail is to be raised above the inner rail.

(a) Calculate the angle of banking required for no lateral thrust on the rails.

(b) Calculate the height by which the outer rail should be raised.

(c) If the train moves at 90 km/h on the same track, calculate the lateral force on the outer rail (mass of train = 10⁶ kg).

(d) What is the danger if the train moves too slowly on a banked track?

Q18. In a school physics demonstration, a bucket of water is whirled in a vertical circle of radius 1.2 m.

(a) Calculate the minimum speed at the top so that water does not spill.

(b) If the speed at the top is 5 m/s, calculate the normal reaction on the water by the bucket.

(c) Calculate the tension in the arm at the lowest point if the speed there is 6 m/s (mass of bucket + water = 2 kg).

(d) Explain why water stays in the bucket even when upside down at sufficient speed.

(e) What happens if the speed at the top falls below the minimum?