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Physics Chapter 4 : Topic 10
Torque and Angular Acceleration
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Torque is the rotational equivalent of:
Reasoning: Force produces linear acceleration, while torque produces angular acceleration.
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The turning effect of a force about an axis is called:
Reasoning: Torque is the rotational effect produced by a force.
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The SI unit of torque is:
Reasoning: $\mathbf{\tau}\mathbf{=}\mathbf{F}\mathbf{\times}\mathbf{r}$ $\mathbf{\Longrightarrow}$ Unit: $\mathbf{N \times m = Nm}$
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Torque depends on:
Reasoning: $\mathbf{\tau}\mathbf{=}\mathbf{F}\mathbf{\times}\mathbf{r}$ ; where$\ \mathbf{r}$ is perpendicular distance.
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A force produces maximum torque when it acts:
Reasoning: Maximum torque occurs when angle between force and radius is $\mathbf{90}^{\mathbf{o}}$.
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If the line of action of force passes through the axis of rotation, torque is:
Reasoning: Perpendicular distance from axis becomes zero.
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Increasing the lever arm of a force will:
Reasoning: $\mathbf{\tau}\mathbf{=}\mathbf{Fr}$ ; Torque increases with distance.
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Newton’s second law for rotational motion is:
Reasoning: Torque produces angular acceleration in rotational motion.
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The rotational equivalent of mass in Newton’s second law is:
Reasoning: Moment of inertia resists angular acceleration like mass resists linear acceleration.
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The rotational equivalent of linear acceleration is:
Reasoning: Angular acceleration represents change in angular velocity.
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For a particle rotating about an axis, torque is:
Reasoning: $\mathbf{\tau}\mathbf{=}\mathbf{Fr}$
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The relation between torque and angular acceleration shows that:
Reasoning: Torque is responsible for changing rotational motion.
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The equation $\mathbf{\tau}\mathbf{=}\mathbf{I\alpha}$ is obtained by replacing:
Reasoning: It is the rotational form of Newton’s second law.
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According to $\mathbf{\tau}\mathbf{=}\mathbf{I\alpha}$ angular acceleration is directly proportional to:
Reasoning: $\mathbf{\alpha}\mathbf{=}$ $\frac{\mathbf{\tau}}{\mathbf{I}}$
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If torque is doubled while moment of inertia remains constant, angular acceleration:
Reasoning: $\mathbf{\alpha}\mathbf{=}$ $\frac{\mathbf{\tau}}{\mathbf{I}}$ $\mathbf{\Longrightarrow}$ $\mathbf{\alpha}\mathbf{\propto}\mathbf{\tau}$
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If moment of inertia is doubled while torque remains constant, angular acceleration:
Reasoning: $\mathbf{\alpha}\mathbf{=}$ $\frac{\mathbf{\tau}}{\mathbf{I}}$ $\mathbf{\Longrightarrow}$ $\mathbf{\alpha}\mathbf{\propto}$ $\frac{\mathbf{1}}{\mathbf{I}}$
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A body with large moment of inertia requires:
Reasoning: Greater rotational resistance requires greater torque.
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For the same torque, which object has greater angular acceleration?
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A torque of $\mathbf{20\ Nm}$ acts on a body having moment of inertia $\mathbf{5\ }\mathbf{kg\ m}^{\mathbf{2}}$. Angular acceleration is:
Reasoning: $\mathbf{\alpha}\mathbf{=}$ $\frac{\mathbf{\tau}}{\mathbf{I}}\mathbf{=}\frac{\mathbf{20}}{\mathbf{5}}\mathbf{=}\mathbf{4\ }\mathbf{rad/s}^{\mathbf{2}}$
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A wheel has moment of inertia $\mathbf{10\ }\mathbf{kg\ m}^{\mathbf{2}}$ and angular acceleration $\mathbf{3\ }\mathbf{rad/s}^{\mathbf{2}}$. Torque acting on it is:
Reasoning: $\mathbf{\tau}\mathbf{=}\mathbf{I\alpha}$ $\mathbf{= 10(3) = 30\ Nm}$
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A torque of $\mathbf{50\ Nm}$ produces angular acceleration of $\mathbf{5\ }\mathbf{rad/s}^{\mathbf{2}}$. Moment of inertia is:
Reasoning: $\mathbf{I}\mathbf{=}$ $\frac{\mathbf{\tau}}{\mathbf{\alpha}}\mathbf{=}\frac{\mathbf{50}}{\mathbf{5}}\mathbf{=}\mathbf{10\ }\mathbf{kg\ m}^{\mathbf{2}}$
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If torque becomes zero, angular acceleration becomes:
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A flywheel has moment of inertia $\mathbf{20\ }\mathbf{kg\ m}^{\mathbf{2}}$. A torque of $\mathbf{100\ Nm}$ acts on it. Its angular acceleration is:
Reasoning: $\mathbf{\alpha}\mathbf{=}$ $\frac{\mathbf{\tau}}{\mathbf{I}}\mathbf{=}\frac{\mathbf{100}}{\mathbf{20}}\mathbf{=}\mathbf{5\ }\mathbf{rad/s}^{\mathbf{2}}$
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A door handle is placed far from the hinges because:
Reasoning: $\mathbf{\tau}\mathbf{=}\mathbf{F}\mathbf{\times}\mathbf{r}$ $\mathbf{\Longrightarrow}$ $\mathbf{\tau}\mathbf{\propto}\mathbf{r}$ ; where$\ \mathbf{r}$ is perpendicular distance.Larger distance increases turning effect.
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A mechanic uses a longer wrench because it:
Reasoning: $\mathbf{\tau}\mathbf{=}\mathbf{F}\mathbf{\times}\mathbf{r}$ $\mathbf{\Longrightarrow}$ $\mathbf{\tau}\mathbf{\propto}\mathbf{r}$ ; where$\ \mathbf{r}$ is perpendicular distance.Greater lever arm produces greater torque.
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A heavy flywheel is difficult to start rotating because:
Reasoning: Large $\mathbf{(}\mathbf{I}\mathbf{)}$ resists changes in rotational motion.
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A skater pulls arms inward and spins faster because:
Reasoning: Smaller moment of inertia allows faster rotation.
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A rotating object slows down when:
Reasoning: Opposing torque reduces angular velocity.
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Two bodies experience the same torque. The body with smaller moment of inertia will have:
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The equation $\mathbf{(}\mathbf{\tau = I\alpha}\mathbf{)}$ is similar to $\mathbf{(}\mathbf{F = ma}\mathbf{)}$ because:
Reasoning: They are equivalent laws for different types of motion.
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If the mass of a rotating body is moved farther from the axis:
Reasoning: Greater radius increases $\mathbf{(}\mathbf{I)}$.
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A body has large angular acceleration when:
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The dimensional formula of torque is:
Reasoning: $\mathbf{\tau}\mathbf{=}\mathbf{Fr}\mathbf{=}\left( \mathbf{M\ L\ }\mathbf{T}^{\mathbf{- 2}} \right)\mathbf{(L) = M\ }\mathbf{L}^{\mathbf{2\ }}\mathbf{T}^{\mathbf{- 2}}$
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Angular acceleration is measured in:
Reasoning: Angular acceleration is change in angular velocity per unit time.
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A force produces rotation only when:
Reasoning: Only perpendicular force produces torque.
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The correct statement about rotational dynamics is:
Reasoning: The fundamental relation is $\mathbf{\tau}\mathbf{=}\mathbf{I\alpha}$.
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