*This preview shows
page 1. Sign up
to
view the full content.*

**Unformatted text preview: **r
path of radius r with constant angular velocity ω . Suppose that at time t, the object has swept
out an angle measuring θ radians. If we assume that the object is at the point (r, 0) when t = 0,
the angle θ is in standard position. By deﬁnition, ω = θ which we rewrite as θ = ωt. According
t
to Theorem 10.3, the location of the object Q(x, y ) on the circle is found using the equations
x = r cos(θ) = r cos(ωt) and y = r sin(θ) = r sin(ωt). Hence, at time t, the object is at the point
(r cos(ωt), r sin(ωt)).11
y
r Q (x, y ) = (r cos(ωt), r sin(ωt)) 1 θ = ωt
1 rx Equations for Circular Motion
Example 10.2.7. Suppose we are in the situation of Example 10.1.5. Find the equations of motion
of Lakeland Community College as the earth rotates.
π
Solution. From Example 10.1.5, we take r = 2960 miles and and ω = 12 hours . Hence, the
π
π
equations of motion are x = r cos(ωt) = 2960 cos 12 t and y = r sin(ωt) = 2960 sin 12 t , where x
and y are measured in miles and t is measured in hours. In addition to circular motion, Theorem 10.3 is also the key to developing what is usually called
‘right triangle’ trigonometry.12 As we...

View
Full
Document