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AQA A-Level Further Mathematics
Optional Application 1 – Mechanics
3.6 Moments of Inertia
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Moment of inertia depends on the object's mass and its distribution relative to the axis of
rotation
The units of moment of inertia are
kg
The parallel axis theorem is used to calculate the moment of inertia about an axis through the center of mass.
False
Match the theorem with its application:
Parallel Axis Theorem ↔️ Calculating \(I\) about a parallel axis
Perpendicular Axis Theorem ↔️ Calculating \(I_z\) for 2D objects
Mass distribution significantly affects moment of inertia.
True
The larger the moment of inertia, the more
difficult
it is to alter an object's angular velocity.
Objects with mass concentrated at larger distances from the axis of rotation have higher
moments of inertia
.
True
What is the formula for the parallel axis theorem?
I
=
I =
I
=
I
C
M
+
I_{CM} +
I
CM
+
m
d
2
md^{2}
m
d
2
The perpendicular axis theorem applies only to two-dimensional
objects
The parallel and perpendicular axis theorems are essential for calculating moments of inertia about different
axes
.
True
The perpendicular axis theorem applies to
two-dimensional
objects only.
The distance \(d\) in the parallel axis theorem is the distance between parallel axes.
True
What does \(r\) represent in the moment of inertia formula?
Distance from axis of rotation
What does \(d\) represent in the parallel axis theorem?
Distance between parallel axes
The greater the moment of inertia, the easier it is to change an object's angular velocity.
False
Match the shape with its moment of inertia:
Solid Sphere ↔️ \frac{2}{5}mr^2</latex>
Thin Ring ↔️
m
r
2
mr^{2}
m
r
2
Solid Cylinder ↔️
1
2
m
r
2
\frac{1}{2}mr^{2}
2
1
m
r
2
The parallel axis theorem formula is
I
= I_{CM} + md^{2}
Moment of inertia
measures an object's
resistance
to changes in its
rotational motion
about an
axis
.
rotational
The axis of rotation determines how mass is
distributed
Arrange the following scenarios based on increasing resistance to rotation:
1️⃣ Solid Sphere
2️⃣ Solid Cylinder
3️⃣ Thin Ring
Higher moments of inertia indicate greater resistance to changes in rotational
motion
In the parallel axis theorem, 'm' represents the
mass
of the object.
True
What does \(I_{CM}\) represent in the parallel axis theorem?
Moment of inertia about center of mass
What is the formula for the parallel axis theorem?
I
=
I =
I
=
I
C
M
+
I_{CM} +
I
CM
+
m
d
2
md^{2}
m
d
2
What are \(I_x\) and \(I_y\) in the perpendicular axis theorem?
Moments of inertia about orthogonal axes
What does moment of inertia measure in rotational motion?
Resistance to changes in angular velocity
Objects with more mass concentrated at larger distances from the axis have higher
moments of inertia
.
True
What does moment of inertia measure?
Resistance to rotational change
What is the formula for calculating moment of inertia?
I
=
I =
I
=
m
r
2
mr^{2}
m
r
2
Arrange the shapes by increasing resistance to rotation (least to most):
1️⃣ Solid Sphere
2️⃣ Solid Cylinder
3️⃣ Thin Ring
What type of objects does the perpendicular axis theorem apply to?
Two-dimensional objects
What is the formula for moment of inertia?
I = mr^2</latex>
Understanding moment of inertia is essential for analyzing
rotational dynamics
.
True
Moment of inertia is crucial for analyzing torque, energy, and rotational
dynamics
The parallel axis theorem allows you to calculate the moment of inertia about an axis parallel to one that passes through the
center
of mass.
What does 'd' represent in the parallel axis theorem?
Distance between parallel axes
The perpendicular axis theorem applies only to
two-dimensional
objects.
What is the formula for the perpendicular axis theorem?
I
z
=
I_{z} =
I
z
=
I
x
+
I_{x} +
I
x
+
I
y
I_{y}
I
y
Match the theorem with its application and formula:
Parallel Axis ↔️ Calculating \(I\) about a parallel axis ||| \(I = I_{CM} + md^2\)
Perpendicular Axis ↔️ Calculating \(I_z\) for 2D objects ||| \(I_z = I_x + I_y\)
The formula for moment of inertia is
mr^2
.
See all 41 cards
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