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Various aspects of rotational motion, including torque, angular momentum, and conservation of angular momentum. It also introduces elasticity and elastic moduli, such as young's modulus, shear modulus, and bulk modulus. Students will learn about the relationships between torque, angular momentum, and elasticity, as well as the concepts of work and power in rotational motion.
Typology: Study notes
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N
F
-> tangential acceleration: F (^) t = mat
Rotational motion description:
In general: Στ =Ια
2 t t t
a F r ma r mr I r
τ= = = = α
Angular momentum L relative to the origin O:
Cross product of the particle position r and linear momentum p
L = r x p
Each particle of the object rotates in the xy plane about the z axis with an angular speed of ω Angular momentum of an individual particle: Li = mi r (^) i^2 ω
Sum over all particles: 2 z i i i i i
Work done by F on the object as it rotates through an infinitesimal distance ds = r d θ dW = F.^ d s = ( F sin φ) r d θ dW = τ d θ
Note: Both work and torque have units of Nm – but remember: torque is not an energy!!
θ
Multiwalled Carbon nanotubes
Figure by Narupon Chattrapiban
Shape of Wavefront
Elastic Moduli describe how materials respond to forces
Measures: Resistance of a solid to a change in its length
A bar (surface area A) is stretched by an amount Δ L under the action of the force F
The tensile stress =
The tensile strain =
i
tensile stress tensile strain i
F Y A L L
≡ = Δ
Measures: Resistance to relative motion of parallel planes within a solid
The shear stress =
The shear strain = shear stress shear strain
x h
x h
