Difference between revisions of "Forest UCM Homework"
| Line 1: | Line 1: | ||
=Chapt 1= | =Chapt 1= | ||
| − | 1.10) A particle moves in a circle (center O and radius R) with constant angular velocity \omega counter-clockwise. The circle lies in the x-y plane and the particle is on the x axis at time t=0. Show the the particle's position is given by | + | 1.10) A particle moves in a circle (center O and radius R) with constant angular velocity <math>\omega</math> counter-clockwise. The circle lies in the x-y plane and the particle is on the x axis at time t=0. Show the the particle's position is given by |
| − | : \vec{r}(t) = R \left ( \cos(\omega t) \hat{i} \sin(\omega t) \hat j \right) | + | :<math> \vec{r}(t) = R \left ( \cos(\omega t) \hat{i} \sin(\omega t) \hat j \right)</math> |
Find the particle's velocity and acceleration. What are the magnitude and direction of the acceleration? Relate your results to well-known properties of uniform circular motion | Find the particle's velocity and acceleration. What are the magnitude and direction of the acceleration? Relate your results to well-known properties of uniform circular motion | ||
Revision as of 04:16, 16 August 2014
Chapt 1
1.10) A particle moves in a circle (center O and radius R) with constant angular velocity counter-clockwise. The circle lies in the x-y plane and the particle is on the x axis at time t=0. Show the the particle's position is given by
Find the particle's velocity and acceleration. What are the magnitude and direction of the acceleration? Relate your results to well-known properties of uniform circular motion
,1.15, 1.17,1.18,1.21,1.24 1.26)
1.35.)A golf ball is hit from ground level with speed v_0 in a direction that is due east and at an angle of \theta above the horizontal. Neglecting air resistance, use Newton's second law to find the position as a finction of tme, using coordiates with x measured east, y nore, and z vertiaclly up. Find the time for the golf ball to return to the ground and how far it travels in that time.
1.37.) A student kicks a frictionless puck with initial speed v_0, so that it slides staight up a plane that is inclined at an angle \theta above the horizontal. (a) Write down Newton's second law for the puck and solve to give its position as a function of time.(b) How long will the puck take to return to its starting point?
1.26, 1.35, 1.36, 1.37, 1.38, 1.46
1.26,1.27,1.35,1.36,1.37,