11 Questions
What is the relationship between degrees and radians?
1 degree = π/180 radians
What is the formula for linear velocity in circular motion?
v = ω/r
What is the unit of angular velocity?
radians per second (rad/s)
What does centripetal acceleration represent?
Acceleration directed toward the center of the circle
What is the formula for centripetal force?
Answers A and C
What does angular velocity represent in circular motion?
The change in angle per unit time
What quantity does the period of an object's motion represent?
Time taken for one revolution
What happens to an object's velocity in uniform circular motion?
Remains constant in magnitude but changes direction
What does centripetal acceleration provide for an object in circular motion?
It provides the force that causes the object to move in a circle.
What is the formula to convert from degrees to radians?
Multiply by $\frac{\pi}{180}$
What is the SI unit for centripetal acceleration?
$m s^{-2}$
Study Notes
Angle Measurements
- Angles are measured in both degrees and radians
- 1° = 1/360 of a full circle
- To convert from degrees to radians, multiply by π/180
Linear Velocity
- Linear velocity (v) is the speed of a particle in a direction perpendicular to the radius at that point
- v = ωr
- Unit of linear velocity: ms-1
Angular Velocity
- Angular velocity (ω) is the rate of change of angle with respect to time
- ω = θ/t
- Unit of angular velocity: rad/s
Periodic Time
- Periodic time (T) is the time taken for one complete revolution, cycle or oscillation
- T = 2πr/v
- T = 2π/ω
- Unit of periodic time: seconds (s)
Centripetal Acceleration
- Centripetal acceleration is the acceleration of an object traveling in uniform circular motion
- It is directed towards the centre of the circle
- Vector quantity with unit: m/s²
Centripetal and Centrifugal Forces
- Centripetal force is the force required to maintain uniform circular motion
- It is directed towards the centre of the circle
- Vector quantity with unit: newton (N)
- Centrifugal force is the force outward due to an object moving in circular motion
- The centripetal force is balanced by a reaction force, the centrifugal force
This quiz covers conversions between degrees and radians, as well as formulas for calculating angle in radians, linear velocity, and angular velocity in circular motion. Test your understanding of arc length and radius relationships, linear velocity calculations, and angular velocity concepts.
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