The topic is all about theAngular Motion of Particles.Please use pen and paper to solve and also use three decimal places. Please show the conversion solution. Thank you.
Here are the formulas and discussion:
θ=θ_o+ω_o t+1/2 αt^2
ω=ω_0+αt
ω^2=ω_o^2+2α(θ-θ_o)
considering the tangential and normal components of the acceleration in a curvilinear motion of particles:
a_t=rα
a_n=rω^2=vω
The angular motion may be derived from the translational motion of particles by considering the given circle:
s=rθ
ds/dt=r dθ/dt or
v=rω
dv/dt=r dω/dt ora=rα
P.S. I provide also the answer but show me the complete solution on how to get that answer
Extracted text: rad The constant angular acceleration of the rotating disk is a = 12. The angular velocity of the disk is 24ra, clockwise, when t = 0. Determine the total angle turned by the disk between t = 0 and t = 4 s.
Extracted text: a = 12 rad/s w = 12t + C1 rad/s 0 = 6t2 + C1t + C2 rad || Initial conditions: 0 = 0, w = -24 rad/s when t 0. .. C1 -24 rad/s and | C2 = 0. ..w = 12t – 24 rad/s 0 = 6t² – 24t rad Note that the rotation reverses direction when t 2 s (obtained by setting w = 0). When t = 0, 0 = 0. When t = 2 s, 0 = 6(2)² – 24(2) : When t = 4 s, 0 = 6(4)² – 24(4) = 0 The total angle turned through is 0tot = 48 rad a -24.0 rad