16 circular motion

Formula for angular velocity

ω = θ/t

formula for linear velocity

v = rω

what is the frequency in circular motion

formula linking frequency and angular velocity

the number of complete revolutions per second

ω = 2πf

what is the period of an object in circular motion

formula linking period and angular velocity

the time taken for a complete revolution

ω = 2π/T

What is centripetal force?

what direction does it act?

any force that causes an object to move in a circular path, which is always perpendicular to the velocity of the object; acting towards the centre of the circle

for objects with the same angular velocity, what is the relationship between linear velocity and the radius

v ∝ r

why is centripetal acceleration constantly changing?

what direction does it act?

acceleration is the rate of change in velocity, and since velocity is changing, so is acceleration, so you get centripetal acceleration

- always acts toward the centre of the circle

formulas for centripetal acceleration

a = v²/r

a = ω²r

formulas for centripetal force?

what direction does it act?

F = mv²/r

F = mω²r

acts towards centre

for a body in centripetal motion, is there any work done?

explain why

The force changes the direction of motion; velocity remains perpendicular to force, so the object doesn't move toward or away from the centre of the circle so there is no motion in the direction of force hence, no work is done on the object so the objects KE and therefore speed remains constant

how can we investigate circular motion (6 marks) ?

- attach a rubber bung to one end of a string and thread the string through a glass tube. at the other end, tie some washers to act as a weight. the washers provide tension in the string, which acts as the centripetal force

- mark a point on the string and measure the distance from this mark to the centre of the bung. this distance is the radius (r) of the circular motion. spin the bung in a horizontal circle by holding the glass tube, adjusting the speed so the mark stays level with the top of the tube. this ensures the tension in the string matches the weight of the washers.

measure the time for the bung to complete one circle (T). To improve accuracy, time 10 circles and divide by 10 for an average. use the time period to calculate angular velocity, then the centripetal force.

F should = W

repeat the experiment with different radii by adjusting the mark on the string. You'll observe that as r increases, the time period increases but the centripetal force remains constant.