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Chapter 9 : Rotational Motion, image, CHEE ZI QING A20SC0043 - Coggle…
Chapter 9 : Rotational Motion
Angular Quantities
l =Rθ, l= arc length, R= radius of the circle
only radian form can be used in calculation
acceleration
Tangential acceleration, atan= Δv/Δt= Rα= R (dω/dt)
Centripetal acceleration, ac=v^2/(r)=r(ω^2)
angular acceleration, α=Δω/Δt
instantaneous angular acceleration,α=limΔt→0Δω/Δt=dω/dt
velocity
Average angular velocity, ω=Δθ/Δt ω = Δ θ / Δ t
Linear velocity,v= Rω
Instantaneous angular velocity, ω=limΔt→0Δω/Δt=dθ/dt
tangential velocity,v =rω
frequency (Hz)= 1/T,time= ω/2pi
Vector Nature of Angular Quantities
Angular momentum and angular velocity= vertor quantities (magnitude+direction)
a point on a rotating wheel is constantly rotating and changing direction.
Constant Angular Acceleration
Torque
Torque,T = FR = Iα
unit for torque= kg m^2 s^-2 or Nm
Rotational Dynamics; Torque and Rotational Dynamics
Rotational Inertia, I=m(R^2)
unit for I =kg m^2
Rotational Inertia depends on =mass , the location of the axis of rotation
Solving Problems in Rotational Dynamics
Determining Moments of Inertia
parallel axis theorem :pencil2: I = Icm + Mh^2
perpendicular axis theorem (flat object) :pencil2: Iz = Ix + Iy
Rotational Kinetic Energy
Kinetic energy, K = 1/2 Mv^2 (tranlational motion) + 1/2 Iω^2 (rotational motion)
Rotational Plus Translational Motion; Rolling
Rolling= Rotational + Translational Motion
Why does a Rolling Sphere slow down
Frictional force = angular speed of the sphere would increase
No ideal sphere (perfectly spherical)
Relationship between translational and Rotational formula
CHEE ZI QING A20SC0043
