Equations of rotational motion and comparison with linear motion - One Line Questions
1.
The relationship between angular acceleration (α) and linear acceleration (a) for a point at a distance r from the axis of rotation is: —
a = αr
2.
Which of the following statements is analogous to 'an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force'? —
A rotating body continues to rotate with the same angular velocity unless acted upon by a net torque.
3.
Which of the following is the rotational analogue of linear velocity? —
Angular velocity
4.
The rotational analogue of linear momentum (p=mv) is: —
Angular momentum (L=Iω)
5.
The rotational analogue of impulse (J = FΔt) is: —
Angular impulse (τΔt)
6.
Which physical quantity is the rotational analogue of linear acceleration? —
Angular acceleration
7.
Which quantity is conserved if no external torque acts on a system? —
Angular momentum
8.
Which of the following is a scalar quantity? —
Angular displacement
9.
The rotational analogue of displacement (s) is: —
Angular displacement (θ)
10.
Consider a rigid body rotating about a fixed axis. If the net external torque is zero, then: —
Angular acceleration is zero
11.
The rotational analogue of momentum conservation (if net force is zero, momentum is conserved) is: —
Conservation of angular momentum (if net torque is zero, angular momentum is conserved).
12.
If a net torque acts on a rigid body, it causes: —
Angular acceleration
13.
If the moment of inertia of a body decreases, and its angular momentum remains constant, what happens to its angular velocity? —
Increases
14.
The magnitude of angular momentum of a rigid body rotating about a fixed axis is given by: —
I * ω
15.
If the linear velocity of a point on a rotating object is doubled, what happens to its angular velocity, assuming the radius remains constant? —
It remains the same
16.
Which equation correctly compares the rotational kinetic energy to linear kinetic energy? —
KE_rotational = 1/2 Iω^2 and KE_linear = 1/2 mv^2
17.
In the equation τ = Iα, what does 'I' represent? —
Moment of inertia
18.
If a body is rotating with constant angular acceleration, its angular velocity changes: —
Linearly with time
19.
The SI unit of angular velocity is: —
rad/s
20.
Which quantity is the rotational analogue of mass? —
Moment of inertia
21.
Which quantity represents the 'effort' required to change the rotational state of motion of a body? —
Torque
22.
Which of the following is a vector quantity? —
Angular velocity
23.
The rotational analogue of force (F) is: —
Torque (τ)
24.
If a body is rotating with constant angular velocity, what is its angular acceleration? —
Zero
25.
The comparison between linear and rotational motion equations is valid under which condition? —
When the body is rigid and the acceleration is constant
26.
Power in rotational motion is given by P = τω. What is the linear analogue of this equation? —
P = Fv
27.
The SI unit of angular acceleration is: —
rad/s^2
28.
The relationship between angular displacement (θ) and the arc length (s) subtended at the circumference of a circle of radius r is: —
s = rθ
29.
If the angular displacement is plotted against time for a body undergoing constant angular acceleration starting from rest, the graph will be a: —
Parabola
30.
If a body is initially at rest and a constant torque is applied, its angular displacement is proportional to: —
t^2
31.
In the context of rotational motion, what does 'rigid body' imply? —
The distance between any two particles in the body remains constant
32.
The unit of angular impulse is equivalent to the unit of: —
Angular momentum
33.
The equation τ = dL/dt directly relates: —
Torque and angular momentum
34.
The rotational analogue of potential energy is not directly defined in the same way as linear motion, but changes in angular position can be related to potential energy in specific contexts like gravity for extended bodies. —
False
35.
The rotational analogue of mass (m) is moment of inertia (I). This analogy holds because both quantities resist changes in motion. —
True
36.
The relationship between angular frequency (ω) in SHM and angular velocity in uniform circular motion is that they are numerically equal, but angular velocity is a vector. —
True
37.
The relationship between angular velocity (ω) and linear velocity (v) for a point at a distance r from the axis of rotation is: —
v = ωr
38.
If a constant torque is applied to a rigid body, its angular acceleration will be: —
Constant
39.
The work done in rotational motion is given by W = τΔθ. What is the linear analogue of this equation? —
W = Fd
40.
If a net torque of zero acts on a rigid body, the body will have: —
Both (a) and (c)
41.
Which equation describes the change in angular momentum (ΔL) due to an applied torque (τ) over a time interval (Δt)? —
ΔL = τ * Δt
42.
Which equation directly relates the change in angular velocity (Δω) to the angular impulse (τΔt) and moment of inertia (I)? —
Δω = (τΔt) / I
43.
The rotational equivalent of the second linear equation of motion (s = ut + 1/2 at^2) is: —
θ = ω_i t + 1/2 αt^2
44.
Which equation correctly shows the relationship between torque (τ), moment of inertia (I), and angular acceleration (α) for a rigid body? —
τ = I * α
45.
Which of the following equations represents the rotational analogue of Newton's second law of motion (F=ma)? —
τ = Iα
46.
Which equation implies that if a body is rotating, it will continue to do so with the same angular velocity unless acted upon by an external torque? —
If τ_net = 0, then α = 0
47.
Which equation represents the rotational analogue of the first equation of linear motion (v = u + at)? —
ω_f = ω_i + αt
48.
Which equation compares to the third linear equation of motion (v^2 = u^2 + 2as) in rotational dynamics? —
ω_f^2 = ω_i^2 + 2αθ
49.
Which of the following is NOT a valid equation of rotational motion under constant angular acceleration? —
ω_f = ω_i + αt^2
50.
Which equation relates the final angular velocity (ω_f), initial angular velocity (ω_i), angular acceleration (α), and angular displacement (θ) without involving time? —
ω_f^2 = ω_i^2 + 2αθ