Circular Motion
immediate
September 29, 2024
**Circular Motion (A-Level Maths)**
Circular motion is an important concept in A-Level Maths, especially in the context of mechanics. It
involves studying objects moving in a circle with constant or variable speeds. Here, we break down the
chapter, focusing on key formulas, concepts, and principles.
—
**1. Angular Displacement and Angular Velocity**
**Angular Displacement (θ)**
- **Definition:** The angle subtended at the center of the circular path by the position vector of a particle
in a certain time interval. - **Units:** Measured in radians (rad). - **Formula:**
s
θ=
r
Where: - s = arc length (distance traveled along the circumference) - r = radius of the circle - θ = angular
displacement (in radians)
**Angular Velocity (ω)**
- **Definition:** The rate of change of angular displacement with respect to time. - **Units:** Radians per
second (rad/s). - **Formula:**
dθ v
ω= =
dt r
Where: - v = linear velocity (tangential speed) - r = radius of the circular path
- **For constant angular velocity:**
2π
ω=
T
Where: - T = time period of one complete revolution - 2π radians = angle for one complete revolution.
—
**2. Linear Velocity (v) and its Relation to Angular Velocity**
**Tangential/Linear Velocity (v)**
- **Definition:** The rate at which an object moves along the circumference of the circle. - **Formula:**
v = ωr
Where: - v = linear velocity - ω = angular velocity - r = radius of the circle
- **Units:** Metres per second (m/s).
**3. Centripetal Force and Centripetal Acceleration**
1
immediate
September 29, 2024
**Circular Motion (A-Level Maths)**
Circular motion is an important concept in A-Level Maths, especially in the context of mechanics. It
involves studying objects moving in a circle with constant or variable speeds. Here, we break down the
chapter, focusing on key formulas, concepts, and principles.
—
**1. Angular Displacement and Angular Velocity**
**Angular Displacement (θ)**
- **Definition:** The angle subtended at the center of the circular path by the position vector of a particle
in a certain time interval. - **Units:** Measured in radians (rad). - **Formula:**
s
θ=
r
Where: - s = arc length (distance traveled along the circumference) - r = radius of the circle - θ = angular
displacement (in radians)
**Angular Velocity (ω)**
- **Definition:** The rate of change of angular displacement with respect to time. - **Units:** Radians per
second (rad/s). - **Formula:**
dθ v
ω= =
dt r
Where: - v = linear velocity (tangential speed) - r = radius of the circular path
- **For constant angular velocity:**
2π
ω=
T
Where: - T = time period of one complete revolution - 2π radians = angle for one complete revolution.
—
**2. Linear Velocity (v) and its Relation to Angular Velocity**
**Tangential/Linear Velocity (v)**
- **Definition:** The rate at which an object moves along the circumference of the circle. - **Formula:**
v = ωr
Where: - v = linear velocity - ω = angular velocity - r = radius of the circle
- **Units:** Metres per second (m/s).
**3. Centripetal Force and Centripetal Acceleration**
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