Recent content by Ursa

for (a) ##T=\frac {2\pi}{\omega}## $$\omega=\frac {2\pi}{T}$$ $$\frac{d \omega}{dt}=\frac {-2\pi}{T^2} \frac {dT}{dt} $$ $$\alpha=\frac {-2\pi}{(2.94*10^-15)^2} = 7.27*10^29 rad/s^2$$ for (b) I'm understand that it's infinity, because the period is increasing indefinitely, so it's slowing...

##\Delta x = vt## (for a=0) so ##0.26 m/ 0.0357 s = 7.28 m/s##

it would turn 1/8th of a rotation I did ##\frac {1}{3.5} * \frac {1}{8}## before and also got ## 0.0357 s## for the arrow to pass through. I did the difficult version because I thought I may have done it wrong the first time when I did it this way.

r=22 cm = 0.022 m 3.5 rev/s L_arrow = 26 cm= 0.026 m first I got the speed in rad $$ 3.5* \frac {2 \pi}{0.022}= 999.6 m/s $$ from there I tried to determine the time the arrow had to pass through the spokes, 1/8 th of the wheel. $$ \frac {2 \pi}{0.022} * \frac {1}{0.8} = 35.7 rad $$...

I first used differentials to find an equation for the displacement. $$6.0t^2+5.0t=13$$ and using the quadratic formula I got time ##t=1.1## I then got ##V_x## from ##6.0t+5.0=v_x=11.6## and ##V_y## from ##7.0t=v_y=7.7## The I got v from ##V=\sqrt {V_x^2 + Vy^2} ## $$\sqrt {11.6^2 + 7.7^2}...

These are the components I came up with ##a_y =2.60 sin 63.0 = 2.32## ##a_x=0## ##a_z =2.60 cos 63.0 = 1.18## ##b_y=0## ##b_x =1.30 sin 51.0 = 1.01## ##b_z =1.3 cos 51.0 = 0.82##

So if I understand my mistake the right answers should be (a) 0.97 m^{2} (b) -1.19 m^{2} (c) -1.90 m^{2} (d) 2.34 m^{2} (e) 73.3° or have I veered way of again?

I tried to find the components of the vectors. ##a_y =2.60 sin 63.0 = 2.32## and assuming the z axis would behave the same as an x-axis ##a_z =2.60 cos 63.0 = 1.18## ##b_z =1.30 sin 51.0 = 1.01## making the same assumption ##b_x =1.3 cos 51.0 = 0.82## I now think I should have switched these...

Thank you, now I understand it a bit better.

So in order to get the answer I should just add ##-49.7+16.2## to get ##-33.5##? Once I grasp how to get ##\vec d_1 \cdot \vec d_2## correct I have the top part, but could you expand on what exactly the denominator is? Will is be the ##d_2## = 8.14 which I calculated in my attempt?

(a) I did (7.07*4.1)-(-7.03*3.94)=56.7 with this method I got this answer correct in my first attempt. (b) This where I seem to have gone wrong. I used a · b = (axbx +ayby) then I used a = sqrt(ax2+ay2) to get a single number for the answer. Filling in the numbers 7.07*-7.03 + 4.94*4.1 =...