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AQA A-Level Further Mathematics
Optional Application 1 – Mechanics
3.4 Circular Motion
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Match the type of circular motion with its example:
Uniform Circular Motion ↔️ Planets orbiting the sun at constant speed
Non-Uniform Circular Motion ↔️ Roller coasters on a loop
What are the two types of acceleration in non-uniform circular motion?
Centripetal and tangential
Why does an object accelerate in uniform circular motion despite constant speed?
Direction changes
Tangential acceleration in non-uniform
circular motion
changes the object's speed.
True
Match the variable in the centripetal acceleration formula with its description:
a
c
a_{c}
a
c
↔️ Centripetal acceleration
v
v
v
↔️ Speed of the object
r
r
r
↔️ Radius of the circular path
The centripetal acceleration in circular motion is inversely proportional to the
radius
What does angular velocity measure in circular motion?
Rate of change of angle
What type of acceleration is present in uniform circular motion?
Centripetal acceleration
What is the role of centripetal force in circular motion?
Maintains circular path
What provides the centripetal force for planets orbiting the sun?
Gravitational force
Circular motion refers to the movement of an object along a circular
path
In non-uniform
circular motion
, both speed and direction change.
True
In uniform circular motion, the acceleration is called
centripetal
acceleration.
Match the type of circular motion with its acceleration:
Uniform Circular Motion ↔️ Centripetal acceleration
Non-Uniform Circular Motion ↔️ Centripetal and tangential
What is the direction of centripetal acceleration in uniform circular motion?
Toward the center
The formula for centripetal acceleration is
a
c
=
a_{c} =
a
c
=
v
2
r
\frac{v^{2}}{r}
r
v
2
, where
v
v
v
is the speed of the object.
In uniform circular motion, the speed of the object remains constant.
True
In uniform circular motion, the centripetal acceleration is caused by a change in
direction
An example of uniform circular motion is a planet orbiting the
sun
Centripetal force is always directed towards the
center
Centripetal force changes the direction of the object's
velocity
What are the two main types of circular motion?
Uniform and non-uniform
What is constant in uniform circular motion?
Speed
How does the velocity change in uniform circular motion?
Direction changes
In circular motion, acceleration is always parallel to velocity.
False
In non-uniform circular motion, the object's
speed
varies along the circular path.
What is the direction of centripetal force in circular motion?
Toward the center
What is centripetal acceleration directed towards in circular motion?
The center of the circle
What is the alternative formula for centripetal acceleration using angular velocity?
a
c
=
a_{c} =
a
c
=
ω
2
r
\omega^{2} r
ω
2
r
Match the type of circular motion with its characteristics:
Uniform circular motion ↔️ Constant speed, centripetal acceleration
Non-uniform circular motion ↔️ Varying speed, centripetal and tangential accelerations
Centripetal acceleration in uniform circular motion changes the object's speed.
False
Centripetal force is required for centripetal acceleration.
True
A Ferris wheel exhibits non-uniform
circular motion
.
True
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