# IB DP Physics: HL复习笔记6.1.2 Centripetal Force

### Centripetal Force

• An object moving in a circle is not in equilibrium, it has a resultant force acting upon it
• This is known as the centripetal force and is what keeps the object moving in a circle
• The centripetal force (F) is defined as:

The resultant force perpendicular to the velocity, and therefore directed towards the centre of the circle, required to keep a body in uniform circular motion

•  The magnitude of the centripetal force F can be calculated using:

Centripetal force is always perpendicular to the linear velocity (i.e., the direction of travel)

• Where:
• F = centripetal force (N)
• v = linear speed (m s1)
• ⍵ = angular speed (rad s−1)
• r = radius of the orbit (m)
• Note: centripetal force and centripetal acceleration act in the same direction
• This is due to Newton's Second Law
• The centripetal force is not a separate force of its own
• It can be any type of force, depending on the situation, which keeps an object moving in a circular path
• For example, tension, friction, gravitational, electrical or magnetic

Examples of centripetal force

• When solving circular motion problems involving one of these forces, the equation for centripetal force can be equated to the relevant force equation
• For example, for a charged particle travelling in a circle, the centripetal force causing the charged particle to move in a circle is provided by the magnetic force
• Therefore, equating the expressions for centripetal force and magnetic force gives the following:

• Where:
• B = magnetic field strength (T)
• q = charge on the particle (C)
• m = mass of the particle (kg)
• v = speed of the particle (m s−1)
• r = radius of orbit (m)

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?

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

Step 3: Rearrange for velocity v

• m cancels from both sides

Step 4: Substitute in values