Reading Time: < 1 minuteTorque (
Angular Momentum (
Rotational Motion: Torque, Angular Momentum, and Energy in A-Level Science
What Is Rotational Motion?
Rotational motion occurs when an object spins around an axis.
Key Concepts in Rotational Motion
Torque (
)
)Torque is the rotational equivalent of force:
![\[ \tau = rF \sin\theta \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-403b7b63cb7c324861d6762b87e916c8_l3.png "Rendered by QuickLaTeX.com")
Where:
- : Torque (
) 
: Lever arm distance (
)
: Force (
)
: Angle between force and lever arm
)
: Lever arm distance (
)
: Force (
)
: Angle between force and lever armAngular Momentum (
)
)Angular momentum describes rotational motion:
![\[ L = I\omega \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-2516049dbb2897782eaccb23033626fa_l3.png "Rendered by QuickLaTeX.com")
Where:
- : Moment of inertia (
) 
: Angular velocity (
)
: Moment of inertia (
)
: Angular velocity (
)Rotational Kinetic Energy
The energy of a rotating object:
![\[ KE_{\text{rot}} = \frac{1}{2}I\omega^2 \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-09df02002f952c536e5db7d08aeddb79_l3.png "Rendered by QuickLaTeX.com")
Real-Life Applications of Rotational Motion
Engineering
- Calculating torque in machines and tools
Sports Science
- Analyzing angular momentum in gymnastics and diving
Astronomy
- Understanding the rotation of planets and stars
Example Problem
A wheel with a moment of inertia of 
rotates at 
. Calculate its rotational kinetic energy.
- Formula:
- Substitute Values:
![\[ KE_{\text{rot}} = \frac{1}{2} \cdot 2.5 \cdot 10^2 = 125 \, \text{J} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-925fb4b14e23cebfc0de78988417e681_l3.png "Rendered by QuickLaTeX.com")
Common Mistakes in Rotational Motion Problems
- Confusing torque with force
- Mixing up angular velocity and linear velocity
- Forgetting to square angular velocity in energy calculations
Practice Questions
- A
lever arm applies a force of 
at 
. Calculate the torque. - Calculate the angular momentum of a rotating object with
and 
. - Describe one real-world application of rotational kinetic energy.
lever arm applies a force of 
at 
. Calculate the torque.
and 
.