Calculating Centripetal Force (Cambridge International A-Level Physics)

Calculating centripetal force

• Centripetal force can be calculated using the equation:

$F=\frac{mv^{2}}{r}$

• Where:

  • $F$ = magnitude of the centripetal force, measured in newtons (N)
  • $m$ = mass of object, measured in kilograms (kg)
  • $v$ = velocity, measured in meters per second (m s^-1)
  • $r$ = radius of circular path, measured in metres (m)

• Another form of the equation can be written using the equation linking linear and angular velocity:

$v=rω$

• Where

  • $ω$ = angular velocity measured in radians per second (rad s^-1)

• Substituting into the first centripetal force equation

$F = \frac{m ( r \\omega )^{2}}{r}$

• Simplify the equation

$F=\frac{mr^{2}ω^{2}}{r}=mrω^{2}$

Centripetal force in circular motion

Centripetal force is always perpendicular to the direction of travel

Worked Example A bucket of mass 8.0 kg is filled with water is attached to a string of length 0.5 m.

What is the minimum speed the bucket must have at the top of the circle so no water spills out?

Answer:

Step 1: Draw the forces on the bucket at the top

Step 2: Calculate the centripetal force

• The weight of the bucket = mg
• This is equal to the centripetal force since it is directed towards the centre of the circle

$mg=\frac{mv^{2}}{r}$

Step 3: Rearrange for velocity v

• m cancels from both sides

$v=\sqrt{gr}$

Step 4: Substitute in values

$v=\sqrt{9.81\times0.5}=2.21ms^{-1}$