this is my 1st excercise with changing tangent acceleration with circular motion, would appreciate if anyone can tell me where im going wrong and what to change(adsbygoogle = window.adsbygoogle || []).push({});

a small body connected to a rod with a length of 2m, r=2m, is moving in a horizontal circular motion, with an angular acceleration of

[tex]\alpha[/tex]=[-[tex]\frac{\Pi^{2}}{12}[/tex]sin[tex]\frac{\Pi}{6}[/tex]t]

time is measured in seconds,

at t=0s the body is at point A (at 12 o clock on a clock face) travelling anti clockwise, and at t=3s it is known v=0(the body stops).

find

a) tangent acceleration (a)

b) actual velovity (v)

c) angular velocity ([tex]\omega[/tex])

d) when will the body return to A(12 o clock position)

e) when will the body reach B (6 o clock position)

---------------------------------------------------

a)

a=[tex]\alpha[/tex]*r

a=[-[tex]\frac{\Pi^{2}}{6}[/tex]sin[tex]\frac{\Pi}{6}[/tex]t]

--------------------------------------------------

b)

v=[tex]\int[/tex]adt=[tex]\int[/tex]=[-[tex]\frac{\Pi^{2}}{6}[/tex]sin[tex]\frac{\Pi}{6}[/tex]t]dt=cos[tex]\frac{\Pi}{6}[/tex]t + C

v(t=3)=0=cos[tex]\frac{\Pi}{2}[/tex] + C ===>C=0

v=\Pi*cos[tex]\frac{\Pi}{6}[/tex]t

----------------------------------------------------

c)

[tex]\omega[/tex]=[tex]\frac{v}{r}[/tex]

[tex]\omega[/tex]=[tex]\frac{\Pi}{2}[/tex]cos[tex]\frac{\Pi}{6}[/tex]t

----------------------------------------------------

d)

now i get stuck, i realise that what i need to to is find the time, t, that the angle of the body relative to point A [tex]\vartheta[/tex], is equal to 0 or 2[tex]\Pi[/tex],

thetha=integral(omega)dt=3sin(pi*t/6)

sin(pi*t/6)=0

pi*t/6=pi*K

t=6K

does this mean that it will rach point A every 6 seconds??

-----------------------------------------------------

e)

Point B

similarily with B but comparing thetha with "pi" 180 degrees, but because of the limits of thetha, because it is limites by sinus' limits, it cannot pass 3, therefore cannot reach pi

have i done something wrong, or is this true and the body will never reach B, ie it will start at A, reach C, at 9 o clock, after 3 seconds, stop, return to A, reach D, at 3 o clock, stop, A....... in a half circular motion

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Circular motion, kinematics

**Physics Forums | Science Articles, Homework Help, Discussion**