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:

4.-Calculating-Centripetal-Force-equation-1

12.2.1.4-Centripetal-force-diagram

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 force12.2.1.4-Table-showing-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:

7.8.5-Centripetal-Magnetic-Force-Equation

  • 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?WE-Centripetal-force-question-image_1

Step 1: Draw the forces on the bucket at the topIMG_48A8FF9B12C7-1

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

Screenshot-2022-01-06-at-2.02.01-pm

Step 3: Rearrange for velocity v

    • m cancels from both sides

Screenshot-2022-01-06-at-2.02.07-pmStep 4: Substitute in values

Screenshot-2022-01-06-at-2.02.13-pm

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