IB Physics Topic A.4.1 Torque and Rotational Motion Revision Notes (HL)

IB Physics Topic A.4.1 Torque and Rotational Motion Revision Notes (HL) | RevisionDojo

Written by official IB examiners

What is Torque?

Definition

Torque

Torque is the rotational equivalent of force. It measures the ability of a force to cause an object to rotate.

It depends on three factors:
1. Magnitude of the Force ($F$)
2. Distance from the Axis ($r$): This is the distance from the axis of rotation to the point where the force is applied, and the perpendicular lever arm is $r\sin\theta$.
3. Angle ($\theta$): The angle between the force and the lever arm.
The formula for torque ($\tau$) is: $$\tau = Fr\sin\theta$$

Note

Units: Torque is measured in newton-meters (N m).
Although this is dimensionally equivalent to a joule, torque is never expressed in joules because it is not a form of energy.

How Torque Works

Maximum Torque:
1. Occurs when the force is perpendicular to the lever arm ($\theta = 90^\circ$), making $\sin\theta = 1$.
2. In this case, $\tau = Fr$.
Zero Torque:
1. If the force acts along the line of the lever arm ($\theta = 0^\circ$ or $180^\circ$), then $\sin\theta = 0$, and the torque is zero.

Example

Consider a wrench turning a bolt.
Applying a force of 50 N at a distance of 0.3 m from the bolt, perpendicular to the wrench, the torque is: $$
\tau = 50 \, \text{N} \times 0.3 \, \text{m} \times \sin 90^\circ = 15 \, \text{N m}
$$

Tip

To maximize torque, apply the force as far from the axis as possible and perpendicular to the lever arm.

Equilibrium Conditions: Translational and Rotational

For an object to be in equilibrium, it must satisfy two conditions:

Translational Equilibrium: The net force acting on the object is zero.
Rotational Equilibrium: The net torque acting on the object is zero.

Translational Equilibrium

Definition

Translation equilibrium

An object is in translational equilibrium when the sum of all the external forces acting on the object equals zero.

In other words, the object remains at rest or moves with constant velocity.
Mathematically, this is expressed as: $$\sum \vec{F} = 0$$

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What is Torque?

Definition

Torque

Torque is the rotational equivalent of force. It measures the ability of a force to cause an object to rotate.

It depends on three factors:
1. Magnitude of the Force ($F$)
2. Distance from the Axis ($r$): This is the distance from the axis of rotation to the point where the force is applied, and the perpendicular lever arm is $r\sin\theta$.
3. Angle ($\theta$): The angle between the force and the lever arm.
The formula for torque ($\tau$) is: $$\tau = Fr\sin\theta$$

Note

Units: Torque is measured in newton-meters (N m).
Although this is dimensionally equivalent to a joule, torque is never expressed in joules because it is not a form of energy.

How Torque Works

Maximum Torque:
1. Occurs when the force is perpendicular to the lever arm ($\theta = 90^\circ$), making $\sin\theta = 1$.
2. In this case, $\tau = Fr$.
Zero Torque:
1. If the force acts along the line of the lever arm ($\theta = 0^\circ$ or $180^\circ$), then $\sin\theta = 0$, and the torque is zero.

Example

Consider a wrench turning a bolt.
Applying a force of 50 N at a distance of 0.3 m from the bolt, perpendicular to the wrench, the torque is: $$
\tau = 50 \, \text{N} \times 0.3 \, \text{m} \times \sin 90^\circ = 15 \, \text{N m}
$$

Tip

To maximize torque, apply the force as far from the axis as possible and perpendicular to the lever arm.

Equilibrium Conditions: Translational and Rotational

For an object to be in equilibrium, it must satisfy two conditions:

Translational Equilibrium: The net force acting on the object is zero.
Rotational Equilibrium: The net torque acting on the object is zero.

Translational Equilibrium

Definition

Translation equilibrium

An object is in translational equilibrium when the sum of all the external forces acting on the object equals zero.

In other words, the object remains at rest or moves with constant velocity.
Mathematically, this is expressed as: $$\sum \vec{F} = 0$$

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

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Duis aute irure dolor in reprehenderit

Note

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Tip

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Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics A.4.1 Torque and Rotational Motion Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

What is Torque?

How Torque Works

Equilibrium Conditions: Translational and Rotational

Translational Equilibrium

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What is Torque?

How Torque Works

Equilibrium Conditions: Translational and Rotational

Translational Equilibrium

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

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