The circular movement (MC) is one that is performed by a body in a circular or curvilinear trajectory.
There are important quantities that must be considered when performing this movement, whose velocity orientation is angular. These are the period and the frequency.
The period, which is measured in seconds, is the time span. The frequency, which is measured in hertz, is its continuity, that is, it determines how many times the rotation takes place.
Example: A car may take x seconds (period) to round a roundabout, which it may do one or more times (frequency).
Uniform Circular Movement
Uniform circular motion (MCU) occurs when a body describes a curvilinear path with constant speed.
For example, the fan blades, the blender blades, the Ferris wheel at the amusement park, and the wheels on cars.
Uniformly Varied Circular Movement
The uniformly varied circular motion (MCUV) also describes a curvilinear trajectory, however its speed varies during the course.
Thus, accelerated circular motion is one in which an object comes out of rest and starts to move.
Circular Motion Formulas
Different from linear motions, circular motion adopts another type of magnitude, called angular magnitudes, where the measurements are in radians, namely:
Centripetal force
THE centripetal force is present in circular movements, being calculated using the formula of Newton's Second Law (Principle of dynamics):
Where,
Fç: centripetal force (N)
m: mass (kg)
Theç: centripetal acceleration (m/s2)
centripetal acceleration
THE centripetal acceleration occurs in bodies that follow a circular or curvilinear trajectory, being calculated by the following expression:
Where,
THEç: centripetal acceleration (m/s2)
v: speed (m/s)
r: radius of circular path (m)
Angular Position
Represented by the Greek letter phi (φ), the angular position describes the arc of a part of the trajectory indicated by a certain angle.
φ = S / r
Where,
φ: angular position (rad)
s: position (m)
r: radius of the circle (m)
Angular Displacement
Represented by Δφ (delta phi), the angular displacement defines the final angular position and the initial angular position of the trajectory.
Δφ = ΔS / r
Where,
Δφ: angular displacement (rad)
S: difference between end position and start position (m)
r: radius of the circumference (m).
Average Angular Velocity
THE angular velocity, represented by the Greek letter omega (ω), indicates the angular displacement by the time interval of the movement in the trajectory.
ωm = Δφ / Δt
Where,
ωm: average angular velocity (rad/s)
Δφ: angular displacement (rad)
t. movement time interval(s)
It should be noted that the tangential velocity is perpendicular to the acceleration which, in this case, is centripetal. This is because it always points to the center of the trajectory and is not null.
Average Angular Acceleration
Represented by the Greek letter alpha (α), angular acceleration determines the angular displacement over the time interval of the trajectory.
α = ω / Δt
Where,
α: mean angular acceleration (rad/sec2)
ω: average angular velocity (rad/s)
t: trajectory time interval (s)
See too: Kinematics Formulas
Exercises on circular motion
1. (PUC-SP) Lucas was presented with a fan that, 20s after being turned on, reaches a frequency of 300rpm in a uniformly accelerated movement.
Lucas's scientific spirit made him wonder what the number of turns made by the fan blades during that period of time would be. Using his knowledge of physics, he found
a) 300 laps
b) 900 laps
c) 18000 laps
d) 50 laps
e) 6000 laps
Correct alternative: d) 50 laps.
See too: Physics Formulas
2. (UFRS) A body in uniform circular motion completes 20 turns in 10 seconds. The period (in s) and frequency (in s-1) of the movement are, respectively:
a) 0.50 and 2.0
b) 2.0 and 0.50
c) 0.50 and 5.0
d) 10 and 20
e) 20 and 2.0
Correct alternative: a) 0.50 and 2.0.
For more questions, see theExercises on Uniform Circular Movement.
3. (Unifesp) Father and son ride their bikes and walk side by side at the same speed. It is known that the diameter of the wheels on the father's bicycle is twice the diameter of the wheels on the son's bicycle.
It can be said that the wheels of the father's bicycle turn with
a) half the frequency and angular velocity with which the wheels of the child's bicycle turn.
b) the same frequency and angular velocity with which the wheels of the child's bicycle turn.
c) twice the frequency and angular velocity with which the wheels of the child's bicycle turn.
d) the same frequency as the wheels of the child's bicycle, but with half the angular speed.
e) the same frequency as the wheels of the child's bicycle, but with twice the angular speed.
Correct alternative: a) half the frequency and angular velocity with which the wheels of the child's bicycle turn.
Read too:
- Uniform Movement
- Uniform Rectilinear Movement
- Quantity of Movement
