Question

A ball rolls on a circular track of radius 0.65 m with a constant angular speed of 1.2 rad/s in the counterclockwise direction.

Part A
If the angular position of the ball at t= 0 is theta= 0, find the x component of the ball's position at the time 2.6 s. Let theta= 0 correspond to the positive x direction.

Part B
Find the x component of the ball's position at the time 5.1 s.

Part C
Find the x component of the ball's position at the time 7.6 s.

Answer 1

x=Acos(wt)
x= position
A=amplitude (in a circle radius is always amplitude)
w= angular frequency
t= time(s)

step1: convert rad-> degrees
w=1.2 radians*57.29 (constant)= 68.75degrees

step2: x=Acos(wt)
x=.65m*cos(68.75degrees*time)

just substitute time into equation above

Answer 2

why we use cos instead of sin?