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CAIE A-Level Physics 12.2 Centripetal Acceleration

Practise relating inward acceleration and resultant force in uniform circular motion to speed, radius and the forces acting on the object.

Syllabus
2028–2030
Course
Physics 9702
Level
A2

Exam points

  • explain how a perpendicular constant-magnitude force produces centripetal acceleration and constant-angular-speed circular motion
  • calculate centripetal acceleration using a = rω² or a = v²/r
  • calculate centripetal force using F = mrω² or F = mv²/r and identify the physical force supplying it

Covered syllabus points

12.2.1—A force of constant magnitude that is always perpendicular to the direction12.2.2—Centripetal acceleration causes circular motion with a constant angular12.2.3—A = rω2 and a = v2 / r12.2.4—F = mrω2 and F = mv2 / r

12.2 Centripetal acceleration question 1

[Maximum number: 6]

Question (a)

(a)

A circular metal disc spins horizontally about a vertical axis, as shown in Fig. 1.1.

Fig. 1.1 (not to scale)

Fig. 1.1 (not to scale)

A piece of modelling clay is attached to the disc.
For the instant when the piece of modelling clay is in the position shown, draw on Fig. 1.1:

[ 1 ]

Question (i)

(i)

an arrow, labelled A , showing the direction of the acceleration of the modelling clay.

[ 1 ]

Question (b)

(b)

The metal disc in Fig. 1.1 has a radius of 9.3 cm .

The centre of gravity of the modelling clay is 1.2 cm from the rim of the disc and moves with a speed of 0.68 ms−10.68 \mathrm{~ms}^{-1}.

[ 2 ]

Question (i)

(i)

Calculate the acceleration a of the centre of gravity of the modelling clay.
a= ms−2\mathrm{ms}^{-2}

[ 2 ]

Question (c)

(c)

A second piece of modelling clay is attached to the disc in the position shown in Fig. 1.2.

Fig. 1.2

Fig. 1.2

The second piece of modelling clay has a larger mass than the first piece.
By placing one tick (✓)(\checkmark) in each row, complete Table 1.1 to show how the quantities indicated compare for the two pieces of modelling clay.

Table 1.1

Table 1.1

[ 3 ]

12.2 Centripetal acceleration question 2

[Maximum number: 7]

Question (a)

(a)

With reference to velocity and acceleration, describe uniform circular motion.

[ 2 ]

Question (b)

(b)

Two cars are moving around a horizontal circular track. One car follows path X and the other follows path Y , as shown in Fig. 1.1.

Fig. 1.1 (not to scale)

Fig. 1.1 (not to scale)

The radius of path X is 318 m . Path Y is parallel to, and 27 m outside, path X . Both cars have mass 790 kg . The maximum lateral (sideways) friction force F that the cars can experience without sliding is the same for both cars.

[ 5 ]

Question (i)

(i)

The maximum speed at which the car on path X can move around the track without sliding is 94 m s−194 \mathrm{~m} \mathrm{~s}^{-1}.

Calculate F.
F= N

[ 2 ]

Question (ii)

(ii)

Both cars move around the track. Each car has the maximum speed at which it can move without sliding.

Complete Table 1.1, by placing one tick in each row, to indicate how the quantities indicated for the car on path Y compare with the car on path X .

Table 1.1

Table 1.1

[ 3 ]
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