4 | Circular Motion | IB Physics Content Guide |
Big Ideas
• Objects moving in a circle are experiencing acceleration since the direction of the velocity is constantly changing
• Centripetal acceleration and centripetal force are always directed toward the center of the circle
• The net force for a body in circular motion is equal to the centripetal force
• It is useful to draw a free body diagram to determine what forces are present at a given position
Content Objectives
4.1 – Defining Circular Motion | |
I can convert between angular displacement in revolutions and radians | |
I can describe and calculate the properties of period and frequency | |
I can calculate angular velocity | |
I can describe and calculate tangential velocity based on the angular velocity and radius | |
I can determine the direction and magnitude of centripetal acceleration and centripetal force | |
4.2 – Vertical Circular Motion | |
I can draw correctly proportioned free body diagrams for horizontal and vertical circular motion | |
I can compare the forces on an object at different positions in vertical circular motion | |
I can identify the combination of forces that make up the net force that results in circular motion. | |
I can determine the magnitude and direction of the forces needed to move in a vertical circle | |
4.3 – Circular Motion, Friction, and Angles | |
I can draw a free body diagram when circular motion is produced by a reaction or friction force | |
I can solve problems that involve friction to create circular motion | |
I can solve circular motion problems that incorporate components of an angled force | |
4 | Circular Motion | Shelving Guide |
| Symbol | Unit |
| Draw in vectors for v, ac, and Fc à |
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Distance | d | m |
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Angular Distance | θ | rad |
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Angular Velocity | ω | rad s-1 |
| Data Booklet Equations: | |
Linear Velocity | v | m s-1 |
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Centripetal Acceleration | a | m s-2 |
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Centripetal Force | Fc | N |
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Defining Circular Motion
| Period | T | s | Angular Velocity | ω | rad s-1 |
Time per revolution |
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Vertical Circular Motion
Top:
| Bottom:
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Fnet = Fc = FT + Fg | Fnet = Fc = FT – Fg | ||||
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Top: | Bottom: | ||||
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Fnet = Fc = Fg – R | Fnet = Fc = R – Fg | ||||
Circular Motion with Friction and Angles
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| Relationships between variables:
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| Relationships between variables:
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| Relationships between variables:
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6.1 Circular Motion
Definition: Moving in a perfect circle, while velocity has a constant magnitude but changing direction.
Quantities
Angular displacement (θ): Angle through which the object moves.
Measured in degrees (º) or radians. 2π radians = 360º.
Angular speed (ω): Δθ/Δt.
Period (T): time taken to complete one revolution.
Link between linear and circular quantities: s = θr and v = ωr, where r is the radius.
Centripetal acceleration (ac)
Object moving in a circle:
- Equation: ac = Δv/Δt = vΔ/Δt = vω = v^2/r = 4rπ^2/T^2.
Reason: Since the velocity is changing the direction when an object moves in a circle, there must be an acceleration.
Direction: Always directed towards the center of the circle. It generates the centripetal force, which is also always directed towards the center.
Centripetal force (Fc)
Equation: Fc = mac = (mv^2)/r = mrω^2. No work, as F is perpendicular to v!
Cases:
Satellites in orbit: Centripetal force = Gravitational force, towards the planet’s center of mass.
- Rotor ride: Centripetal force = Gravitational force, towards the planet’s center of mass.
- In this case, Weight force = Friction force.
Turning on a horizontal road: Centripetal force = Friction acting between the tyres and the road.
When skidding: (mv^2)/r = μdmg.
So that it does not skid: (mv^2)/r < μsmg.
Banking on the road: Road banked at an angle θ. Centripetal force = Normal force x sinθ.
Angle proportional to speed.
Examples: cars, cycle velodrome, commercial airline pilots, high-speed trains.
Vertical circle with strings: Weight force and string tension must be taken into account.
At the top: Fc = Tdown + mg
To keep on moving: v^2 = gr.
At the bottom: Fc = Tup – mg.
Maximum tension on the bottom so
that it does not break:
Tbreak > (mv^2)/r + mg
Car on speed bump: Car loses contact when Centripetal force = Weight force, i.e. N = 0.
UNIFORM AND NON-UNIFORM CIRCULAR MOTION
UNIFORM CIRCULAR MOTION
NON-UNIFORM CIRCULAR MOTION
- Angular displacement behaves like vector, when its magnitude is very small. It follows laws of vector addition.
- Angular velocity and angular acceleration are axial vectors.
- Centripetal acceleration always directed towards the centre of the circular path and is always perpendicular to the instantaneous velocity of the particle.
- Circular motion is uniform if aT = rα = 0, that is angular velocity remains constant and radial acceleration
is constant. - When aT or α is present, angular velocity varies with time and net acceleration is
- If aT = 0 or α = 0, no work is done in circular motion.