Velocity and acceleration in circular motion — A/L Combined Mathematics

What must I remember about Velocity and acceleration in circular motion?

• Circular Motion Kinematics: Angular displacement θ (radians), angular velocity ω = dθ/dt (rad/s), and angular acceleration α = dω/dt = d^2θ/dt² (rad/s²).
• Linear-Angular relationships: Linear arc distance s = r*θ; tangential speed v = r*ω; tangential acceleration a_t = r*α.
• Centripetal (Radial) Acceleration: Directed radially inwards toward the circle center: a_r = v² / r = r * ω².
• Total Acceleration in non-uniform circular motion: Vector sum of perpendicular components: a = a_r + a_t; magnitude |a| = √[(v²/r)² + (r*α)²] = √[a_r² + a_t²]; angle with radius tan φ = a_t / a_r.
• Uniform Circular Motion (UCM): When speed v (and ω) is constant: tangential acceleration a_t = 0; only centripetal acceleration a_r = v²/r exists, changing velocity direction continuously without altering speed.

Test yourself (1 minute)

1. Centripetal Force requirement

   By Newton's second law, circular motion requires an inward net resultant force F_c = m * a_r = m*v² / r = m*r*ω² provided by tension, friction, gravity, or normal reaction.

2. Period and Frequency

   Period T = 2π / ω = 2πr / v; Frequency f = 1 / T = ω / (2π).

3. Velocity vector is ALWAYS tangential

   At every instant, the linear velocity vector v is directed along the tangent to the circular path; perpendicular to the position vector r (v · r = 0).

Practise Velocity and acceleration in circular motion questions today

Source: NIE G.C.E. (A/L) Combined Mathematics Resource Book - Applied Mathematics, Unit 3

What comes next?

Next in the syllabus

Where does Velocity and acceleration in circular motion fit in the syllabus?

Year 2 · Term 3