FBISE, NCP & NBF-aligned resources for Classes 9–12
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Physics Chapter 4 : Topic 3
Equations of Angular Motion
1 / 30
The rotational equivalent of linear velocity is:
Reasoning: Angular velocity describes the rate of change of angular displacement, similar to linear velocity.
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The rotational equivalent of linear acceleration is:
Reasoning: Angular acceleration is the rate of change of angular velocity.
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The equation $\mathbf{\omega}_{\mathbf{f}}\mathbf{=}\mathbf{\omega}_{\mathbf{i}}\mathbf{+}\mathbf{\alpha t}$ is used when finding:
Reasoning: This equation relates initial velocity, acceleration, time, and final velocity.
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A wheel starts from rest and has angular acceleration of $\mathbf{4\ }\mathbf{rad/s}^{\mathbf{2}}$. Its angular velocity after $\mathbf{5\ s}$ is:
Reasoning: $\mathbf{\omega}_{\mathbf{f}}\mathbf{=}\mathbf{\omega}_{\mathbf{i}}\mathbf{+}\mathbf{\alpha t}\mathbf{= 0 + (4)(5) = 20\ rad/s}$
5 / 30
If angular acceleration is zero, angular velocity:
Reasoning: Zero angular acceleration means no change in angular velocity.
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The rotational equation equivalent to $\mathbf{v}\mathbf{=}\mathbf{u}\mathbf{+}\mathbf{at\ }$is:
Reasoning: Angular velocity changes with angular acceleration in the same way linear velocity changes with acceleration.
7 / 30
A fan rotating at $\mathbf{10\ r}\mathbf{ad/s}$ increases its angular velocity to $\mathbf{30\ rad/s}$ in $\mathbf{5}$ seconds. Angular acceleration is:
Reasoning: $\mathbf{\alpha}\mathbf{=}$ $\frac{\mathbf{\omega}_{\mathbf{f}}\mathbf{\ - \ }\mathbf{\omega}_{\mathbf{i}}}{\mathbf{t}}\mathbf{=}\frac{\mathbf{30\ - \ 10}}{\mathbf{5}}\mathbf{= 4\ rad/}\mathbf{s}^{\mathbf{2}}$
8 / 30
The equation $\mathbf{\theta}\mathbf{=}\mathbf{\omega}_{\mathbf{i}}\mathbf{t}\mathbf{+}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\alpha}\mathbf{t}^{\mathbf{2}}$ is used to calculate:
Reasoning: It relates displacement with initial angular velocity, acceleration, and time.
9 / 30
A rotating disc starts from rest with angular acceleration $\mathbf{2\ }\mathbf{rad/s}^{\mathbf{2}}$. Its angular displacement after $\mathbf{4\ s}$ is:
Reasoning: $\mathbf{\theta}\mathbf{= 0 +}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{(2)(4}\mathbf{)}^{\mathbf{2}}$ $\mathbf{= 16\ r}\mathbf{ad}$
10 / 30
Which equation does NOT require time to calculate angular displacement?
Reasoning: The third equation relates angular velocity, acceleration, and displacement without time.
11 / 30
A rotating object increases angular velocity from $\mathbf{5\ rad/s}$ to $\mathbf{15\ rad/s}$ while rotating through $\mathbf{50\ rad}$. Angular acceleration is:
Reasoning: $\mathbf{\omega}_{\mathbf{f}}^{\mathbf{2}}\mathbf{=}\mathbf{\omega}_{\mathbf{i}}^{\mathbf{2}}\mathbf{+ 2}\mathbf{\alpha\theta}$ $\mathbf{\Longrightarrow}$ $\mathbf{225 = 25 + 100}\mathbf{\alpha}$ $\mathbf{\Longrightarrow}$ $\mathbf{\alpha}\mathbf{=}\mathbf{2\ }\mathbf{rad/s}^{\mathbf{2}}$
12 / 30
The equation $\mathbf{\omega}_{\mathbf{f}}^{\mathbf{2}}\mathbf{=}\mathbf{\omega}_{\mathbf{i}}^{\mathbf{2}}\mathbf{+ 2}\mathbf{\alpha\theta}$ is similar to:
Reasoning: It is the angular form of the third equation of linear motion.
13 / 30
A motor starts from rest and reaches $\mathbf{100\ rad/s}$ in $\mathbf{20}$ seconds. Its angular acceleration is:
Reasoning: $\mathbf{\alpha}\mathbf{=}$ $\frac{\mathbf{100}}{\mathbf{20}}\mathbf{= 5\ rad/}\mathbf{s}^{\mathbf{2}}$
14 / 30
During uniform rotational acceleration:
Reasoning: Angular motion equations apply when angular acceleration is constant.
15 / 30
A wheel rotating at $\mathbf{20\ rad/s}$ slows down uniformly to $\mathbf{0\ rad/s\ }$in $\mathbf{10\ s}$. Angular acceleration is:
Reasoning: $\mathbf{\alpha}\mathbf{=}$ $\frac{\mathbf{0\ - \ 20}}{\mathbf{10}}\mathbf{= - \ 2\ }\mathbf{rad/s}^{\mathbf{2}}$Negative sign indicates retardation.
16 / 30
Negative angular acceleration represents:
Reasoning: Negative acceleration means angular velocity decreases.
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If a body rotates through $\mathbf{100}$ radians in $\mathbf{5}$ seconds with constant angular velocity, its angular velocity is:
Reasoning: $\mathbf{\omega}\mathbf{=}$ $\frac{\mathbf{\theta}}{\mathbf{t}}\mathbf{=}\frac{\mathbf{100}}{\mathbf{5}}\mathbf{=}\mathbf{20\ rad/s}$
18 / 30
A rotating object has initial angular velocity $\mathbf{10\ rad/s}$ and acceleration $\mathbf{3}\mathbf{\ rad/s}^{\mathbf{2}}$. Angular velocity after $\mathbf{6\ s}$ is:
Reasoning: $\mathbf{\omega}_{\mathbf{f}}\mathbf{= 10 + (3)(6) =}\mathbf{28\ rad/s}$
19 / 30
Angular displacement during uniformly accelerated rotation depends on:
Reasoning: The equation contains all three variables.
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A disc completes $\mathbf{40\ rad}$ displacement in $\mathbf{5}$ seconds. If initial angular velocity is $\mathbf{4\ rad/s}$, angular acceleration is:
Reasoning: $\mathbf{40 = 4(5) +}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\alpha\ }\mathbf{(25)}$ $\mathbf{\Longrightarrow}$ $\mathbf{20 = 12.5\ }\mathbf{\alpha}$ $\mathbf{\Longrightarrow}$ $\mathbf{\alpha}\mathbf{=}\mathbf{1.6\ }\mathbf{rad/s}^{\mathbf{2}}$
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Which quantity is equivalent to displacement in rotational motion?
Reasoning: Angular displacement describes rotational position change.
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The unit of angular acceleration is:
Reasoning: Angular acceleration is change in angular velocity per second.
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A wheel rotates with constant angular acceleration. Which equation can determine its final angular velocity?
Reasoning: This equation directly gives final angular velocity.
24 / 30
A rotating object has $\mathbf{\omega}_{\mathbf{i}}\mathbf{= 20\ rad/s}$, $\mathbf{\alpha}\mathbf{= - \ 4\ rad/}\mathbf{s}^{\mathbf{2}}$. Time required to stop is:
Reasoning: $\mathbf{\omega}_{\mathbf{f}}\mathbf{=}\mathbf{\omega}_{\mathbf{i}}\mathbf{+}\mathbf{\alpha t}$ $\mathbf{\Longrightarrow}$ $\mathbf{0 = 20 - 4}\mathbf{t}$ $\mathbf{\Longrightarrow}$ $\mathbf{t}\mathbf{= 5s}$
25 / 30
The angular displacement of a freely rotating object can be found without knowing time using:
Reasoning: This equation eliminates time from rotational motion calculations.
26 / 30
If angular velocity doubles while radius remains constant, centripetal acceleration becomes:
Reasoning: $\mathbf{a}\mathbf{=}\mathbf{r}\mathbf{\omega}^{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ Acceleration depends on square of angular velocity.
27 / 30
A rotating body covers equal angular displacements in equal intervals of time. Its motion is:
Reasoning: Equal angular displacement per equal time means constant angular velocity.
28 / 30
The equation $\mathbf{\theta}\mathbf{=}$ $\left( \frac{\mathbf{\omega}_{\mathbf{i}}\mathbf{\ + \ }\mathbf{\omega}_{\mathbf{f}}}{\mathbf{2}} \right)\mathbf{t}$ is valid when:
Reasoning: It uses average angular velocity, applicable for constant acceleration.
29 / 30
A rotating body starts from rest and reaches $\mathbf{12\ rad/s}$ after rotating through $\mathbf{36\ rad}$. Angular acceleration is:
Reasoning: $\mathbf{144 = 0 + 2}\mathbf{\alpha\ }\mathbf{(36)}$ $\mathbf{\Longrightarrow}$ $\mathbf{\alpha}\mathbf{=}\mathbf{2\ }\mathbf{rad/s}^{\mathbf{2}}$
30 / 30
Rotational equations of motion are applicable when:
Reasoning: These equations are derived for uniformly accelerated rotational motion.
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