Motion in a Circle

Question 1

Define angular displacement

Answer 1

Angular displacement is the angle of rotation of a body about an axis in a specific direction from a reference point

Question 2

Define angular velocity

Answer 2

Angular velocity ω is the rate of change of angular displacement
ω = dθ/dt
ω = 2πf = 2π/T

Question 3

Formula for linear velocity

Answer 3

v = rω

Question 4

Formula for centripetal acceleration

Answer 4

a = (v^2)/r = rω^2 = vω

Question 5

Formula for centripetal force

Answer 5

F = ma = (mv^2)/r = mrω^2 = mvω

Question 6

Why is resultant acceleration always pointing towards the centre of the circle?

Answer 6

When a body undergoes circular motion, the resultant force acting on it has a radial component only (centripetal force), but no tangential component. Hence, this resultant force always points towards the centre of the circle. As a result, the resultant acceleration also points towards the centre of the circle.