Rotational dynamics is the study of the rotational motion of objects. The moment of inertia is a measure of an object’s:
a) Rotational velocity
b) Resistance to rotational motion
c) Mass
d) Angular velocity
The unit of angular acceleration in SI is:
a) m/s²
b) rad/s²
c) N·m
d) kg·m²/s
The torque on an object is equal to the product of:
a) Force and distance from the axis of rotation
b) Force and time
c) Angular velocity and moment of inertia
d) Angular acceleration and mass
The moment of inertia for a solid cylinder about its central axis is:
a)
1
2
𝑚
𝑟
2
2
1
mr
2
b)
𝑚
𝑟
2
mr
2
c)
1
4
𝑚
𝑟
2
4
1
mr
2
d)
2
3
𝑚
𝑟
2
3
2
mr
2
1
2
𝑚
𝑟
2
2
1
mr
2
The rotational kinetic energy of an object is given by:
a)
1
2
𝑚
𝑣
2
2
1
mv
2
b)
1
2
𝐼
𝜔
2
2
1
Iω
2
c)
𝐼
𝜔
Iω
d)
𝑚
𝑔
ℎ
mgh
1
2
𝐼
𝜔
2
2
1
Iω
2
The rotational analog of Newton’s second law is:
a)
𝐹
=
𝑚
𝑎
F=ma
b)
𝜏
=
𝐼
𝛼
τ=Iα
c)
𝜔
=
𝜃
𝑡
ω=θt
d)
𝐼
=
𝑚
𝑟
2
I=mr
2
𝜏
=
𝐼
𝛼
τ=Iα
Angular momentum is conserved when there is:
a) No external force acting on the system
b) No external torque acting on the system
c) No external acceleration acting on the system
d) No internal force acting on the system
The moment of inertia for a point mass is given by:
a)
𝐼
=
𝑚
𝑟
I=mr
b)
𝐼
=
𝑚
𝑟
2
I=mr
2
c)
𝐼
=
1
2
𝑚
𝑟
2
I=
2
1
mr
2
d)
𝐼
=
𝑚
𝜔
2
I=mω
2
𝐼
=
𝑚
𝑟
2
I=mr
2
The torque required to maintain constant angular velocity is:
a) Zero
b) Proportional to the angular velocity
c) Inversely proportional to the moment of inertia
d) Equal to the moment of inertia
The formula for work done by torque is:
a)
𝑊
=
𝐹
⋅
𝑑
W=F⋅d
b)
𝑊
=
𝜏
⋅
𝜃
W=τ⋅θ
c)
𝑊
=
𝑚
⋅
𝑔
⋅
ℎ
W=m⋅g⋅h
d)
𝑊
=
𝐼
⋅
𝜔
W=I⋅ω
𝑊
=
𝜏
⋅
𝜃
W=τ⋅θ
If a force of 20 N is applied at a distance of 3 meters from the axis of rotation, the torque is:
a) 60 N·m
b) 30 N·m
c) 10 N·m
d) 100 N·m
Angular velocity is the rate of change of:
a) Force
b) Torque
c) Angular displacement
d) Linear velocity
The unit of angular momentum is:
a) kg·m/s
b) N·m·s
c) kg·m²/s
d) J·s
The moment of inertia of a thin rod about an axis at its end is:
a)
1
12
𝑚
𝐿
2
12
1
mL
2
b)
1
2
𝑚
𝐿
2
2
1
mL
2
c)
1
3
𝑚
𝐿
2
3
1
mL
2
d)
𝑚
𝐿
2
mL
2
1
3
𝑚
𝐿
2
3
1
mL
2
The torque is proportional to the rate of change of:
a) Angular momentum
b) Force
c) Linear momentum
d) Energy
The moment of inertia of a solid sphere about its central axis is:
a)
1
2
𝑚
𝑟
2
2
1
mr
2
b)
2
5
𝑚
𝑟
2
5
2
mr
2
c)
1
3
𝑚
𝑟
2
3
1
mr
2
d)
𝑚
𝑟
2
mr
2
2
5
𝑚
𝑟
2
5
2
mr
2
The angular acceleration of an object is:
a) Directly proportional to the applied force
b) Directly proportional to the torque
c) Inversely proportional to the torque
d) Inversely proportional to the moment of inertia
The angular momentum of a rotating object is zero when:
a) The object is at rest
b) The object has no mass
c) The object is moving in a straight line
d) The object is rotating at constant angular velocity
In a rotating system, the work done by torque is equal to:
a) The change in the object’s linear velocity
b) The change in angular velocity
c) The change in angular displacement
d) The change in kinetic energy
The torque required to stop a rotating object is proportional to:
a) Its angular velocity
b) Its angular acceleration
c) Its moment of inertia
d) The applied force
In the case of a rotating object, its angular momentum is the product of:
a) Mass and velocity
b) Moment of inertia and angular velocity
c) Torque and time
d) Angular displacement and time
The formula for calculating angular velocity is:
a)
𝜔
=
𝑣
𝑟
ω=
r
v
b)
𝜔
=
𝑟
𝑣
ω=
v
r
c)
𝜔
=
𝑣
𝐼
ω=
I
v
d)
𝜔
=
1
2
𝑚
𝑣
2
ω=
2
1
mv
2
𝜔
=
𝑣
𝑟
ω=
r
v
The moment of inertia of a disk is given by:
a)
1
2
𝑚
𝑟
2
2
1
mr
2
b)
𝑚
𝑟
2
mr
2
c)
1
4
𝑚
𝑟
2
4
1
mr
2
d)
1
3
𝑚
𝑟
2
3
1
mr
2
1
2
𝑚
𝑟
2
2
1
mr
2
The rate at which work is done by torque is called:
a) Power
b) Energy
c) Force
d) Angular momentum
If the torque acting on a rotating body is constant, the angular acceleration will be:
a) Constant
b) Increasing
c) Decreasing
d) Zero
In rotational motion, the relationship between torque and angular velocity is:
a) Torque is proportional to the rate of change of angular velocity
b) Torque is inversely proportional to angular velocity
c) Torque is equal to angular velocity
d) Torque and angular velocity are unrelated
The work-energy theorem for rotational motion states that:
a) The work done on an object is equal to its change in rotational kinetic energy
b) The work done on an object is equal to its angular velocity
c) The work done on an object is equal to the change in linear velocity
d) The work done on an object is zero
The principle of conservation of angular momentum applies to a system when:
a) No external force is acting on the system
b) No external torque is acting on the system
c) The system is isolated
d) The system is at rest
