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Mechanics
3. Circular Motion
3.1 Motion in a Circle
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Cards (43)
What is circular motion defined as?
Movement along a circular path
The radius in circular motion is the distance from the center of the circle to the object's
path
In what units is angular displacement measured?
Radians
Angular velocity is measured in radians per
second
The formula relating linear velocity, radius, and angular velocity is
v = r\omega
What is tangential velocity in circular motion?
Velocity along the circular path
The unit of radius is
meters
What is the rate of change of angular displacement called?
Angular velocity
Angular displacement is the angle through which an object moves along its circular
path
What is the formula for angular velocity in terms of angular displacement and time?
ω
=
\omega =
ω
=
Δ
θ
Δ
t
\frac{\Delta \theta}{\Delta t}
Δ
t
Δ
θ
Arrange the properties of circular motion in the correct order based on their relationships:
1️⃣ Angular Displacement (
θ
\theta
θ
)
2️⃣ Angular Velocity (
ω
\omega
ω
)
3️⃣ Linear Velocity (
v
v
v
)
What is linear velocity in circular motion?
Speed along the circumference
The linear velocity and
angular velocity
are related by the formula v = r\omega</latex>
In circular motion, what is the definition of angular velocity?
Rate of rotation
In the formula
v
=
v =
v
=
r
ω
r\omega
r
ω
, v</latex> represents the tangential velocity of the object.
Match the property with its symbol:
Angular Displacement ↔️ \theta
Angular Velocity ↔️ \omega
Linear Velocity ↔️ v
Radius ↔️ r
What is the unit of angular velocity?
radians per second
In the relationship
v
=
v =
v
=
r
ω
r\omega
r
ω
,
v
v
v
and
ω
\omega
ω
are proportional when the radius
r
r
r
is constant
What is linear velocity in circular motion?
Speed along the circumference
Angular velocity is measured in radians per
second
The relationship between linear velocity and angular velocity is
v
=
v =
v
=
r
ω
r\omega
r
ω
Match the velocity with its definition:
Linear velocity ↔️ Speed along the circumference
Angular velocity ↔️ Rate of rotation
What are the units of linear velocity?
m/s
What formula relates linear velocity and angular velocity?
v = r\omega</latex>
In the formula
v
=
v =
v
=
r
ω
r\omega
r
ω
,
r
r
r
represents the radius of the circular path
Linear velocity and angular velocity are proportional when the
radius
is constant.
What is centripetal acceleration?
Acceleration in circular motion
The formula for centripetal acceleration is
a
=
a =
a
=
v
2
r
\frac{v^{2}}{r}
r
v
2
, where
v
v
v
is the linear velocity
What is the formula for centripetal force according to Newton's second law?
F
=
F =
F
=
m
a
ma
ma
Centripetal force is measured in units of
Newtons
What is circular motion?
Movement along a circular path
The radius in circular motion is the distance from the center of the circle to the object's
path
Angular velocity is the rate at which
angular displacement
changes with time.
What is the unit of angular displacement?
Radians
The relationship between angular velocity and angular displacement is
ω
=
\omega =
ω
=
Δ
θ
Δ
t
\frac{\Delta \theta}{\Delta t}
Δ
t
Δ
θ
, where
Δ
θ
\Delta \theta
Δ
θ
is the change in angular displacement
Linear velocity and angular velocity are directly proportional when the
radius
is constant.
What direction does centripetal acceleration always point?
Towards the center
The formula for centripetal acceleration is
a
=
a =
a
=
v
2
r
\frac{v^{2}}{r}
r
v
2
, wherev</latex> is the linear velocity
Match the quantity with its unit:
Centripetal Force ↔️ Newtons
Mass ↔️ Kilograms
Centripetal Acceleration ↔️ m/s²
Steps to solve problems involving circular motion:
1️⃣ Identify the key properties
2️⃣ Apply the relevant formulas
3️⃣ Substitute the given values
4️⃣ Solve for the unknowns
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