QS(a) A centrifuge in Figure Q5(a) is often used for astronaut training activity. The radius arm of the centrifuge is 15m and initially rotates according to 8 = 0.3t² where t is in seconds and o is in radians. (i1) Determine the astronaut's angular velocity and linear speed when t = 3.5 s. (i) Determine the astronaut's magnitude of tangential and normal acceleration when t = 3.5 s. 15m Cockpit X. 2, 2 0 = 0.3t? Figure Q5(a)
You may use these formulas please try not to use other than these formulas
Fundamental Equation of Dynamics
KINEMATICS
Particle Rectilinear motion:
Equations of Motion:
Variable a
?=???? ?=???? ???=???
Constant a = ac ?=?0+??? ?=?0+?0?+12???2 ?2=?02+2??(?−?0)
Particle: Σ?=??
Rigid Body: Σ??=?(??)?
(Plane Motion) Σ??=?(??)?
Σ??=??? or Σ??=Σ(ℳ?)?
Particle Curvilinear Motion:
Cartesian Coordinates (x,y,z) ??=?̇ ??=?̈ ??=? ̇ ??=?̈ ??=?̇ ??=?̈
Polar Coordinates (r,θ,z) ??=? ̇ ??=?̈−??̇2 ??=??̇ ??=??̈+2?̇?̇ ??=?̇ ??=?̈
Normal-Tangential Coordinates (n,t,b)
?=?̇ ; ??=?̇=????? ; ??=?2?
?ℎ??? ?=[1+(??/??)2]32⁄|?2?/??2|
Principle of Work and Energy: ?1+?1−2=?2
Kinetic Energy
Particle: ?=12??2
Rigid Body: ?=12???2+ 12???2
(Plane Motion) or ?= 12???2
Work
Variable Force: ??=∫?cos???
Constant Force: ??=(?cos?)Δ?
Weight: ??=−?Δ?
Spring: ??= −(12??22−12??12)
A couple of Moment: ??=? Δ?
Power and Efficiency ?=????=??, ∈= ???????=???????
Relative Motion ?B=?A+?B/A ?B=?A+?B/A
Rigid Body Motion About a Fixed Axis
Conservation of Energy Theorem ?1+?1=?2+?2
Potential Energy ?=?g+?e
Where:
?g=± Wy, ?e=+12??2
Variable a ?=?????=???? ???=???
Constant a = ac ?=?0+??? ?=?0+?0?+12???2 ?2=?02+2??(?−?0)
Principle of Linear Impulse and Momentum:
Particle : ??1+Σ∫???= ??2
Rigid Body: ?(??)1+Σ∫???= ?(??)2
For Point P
s=θr , v=ωr , a?=αr , a?=ω2r
Relative General Plane Motion-Translating Axes ?B=?A+?B/A(pin)?B=?A+?B/A(pin)
Relative General Plane Motion-Tran. And Rot. Axis ?B=?A+?×?B/A+(?B/A)??? ?B=?A+?̇×?B/A+?×(?×?B/A)+2?×(?B/A)???+(?B/A)???
Kinetics
Mass Moment of Inertia ?=∫?2??
Parallel-Axis Theory ?=??+? ?2
The radius of Gyration ?=√??
Conservation of Linear Momentum: Σ(??)1=Σ(??)2
Coefficient of Restitution ?=(??)2−(??)2(??)1−(??)1
Principle of Angular Impulse and Momentum:
Particle : (??)1+Σ∫????= (??)2
Where ??=(?)(??)
Rigid Body : (??)1+Σ∫????= (??)2
(Plane Motion)
Where ??=??? (??)1+Σ∫????= (??)2
Where ??=???
Conservation of Angular Momentum Σ(?)1=Σ(?)2
![(b)
The 110kg bar OA is supported by a spring at one end while the flywheel has mass of
65kg with the radius of gyration kg = 0.25m. Given that the unstretched length of the
spring is 1.5m. At the instant shown in both Figure Q5(b)(6) and (ii) below,
(i)
Determine their types of motion.
(i)
Construct free body diagrams and kinetic diagrams for both figures. Show the
inertial coordinate system of the bodies.
(111)
List down all the equation of motions for both figures.
-5 m-
2 rad/s
k = 6 N/ml
4 m
Figure Q5(b)(i)
2m
w = 2 rad/s
45°
Figure Q5(b)(ii)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33488049-1422-455e-b50d-4d67f5321948%2F7dec3513-d759-4c97-aac9-c1e3d599fa82%2Fxm2hqxm_processed.png&w=3840&q=75)
![QS(a) A centrifuge in Figure Q5(a) is often used for astronaut training activity. The radius
arm of the centrifuge is 15m and initially rotates according to e = 0.32² where t is in
seconds and e is in radians.
(i)
Determine the astronaut's angular velocity and linear speed when t = 3.5 s.
(1)
Determine the astronaut's magnitude of tangential and normal acceleration
when t = 3.5 s.
15m
Cockpit
9 = 0.3t?
Figure Q5(a)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33488049-1422-455e-b50d-4d67f5321948%2F7dec3513-d759-4c97-aac9-c1e3d599fa82%2Fmxuv5sc_processed.png&w=3840&q=75)
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