You are swinging a sling shot, which is basically a string tied to a rock, vertically as shown. After you get it going fairly fast, you hold your hand stationary so it swings around in a perfect circle. The rock slows down as it gets higher and speeds up as it comes back down. One simple
You are swinging a sling shot, which is basically a string tied to a rock, vertically as shown. After you get it going fairly fast, you hold your hand stationary so it swings around in a perfect circle.
The rock slows down as it gets higher and speeds up as it comes back down. One simple model for how this would work is that the tangential component of the rock's velocity is
vt(t)=v0-(v0/4)sin((2pi/T)t)
where v0 is the rock's speed at t=0s and T is the time it takes the rock to go all the way around the circle. Call
L the length of the string.
1. What is the algebraic expression for the angular speed of the rock?
2. What is the centripetal acceleration of the rock?
3. What is the tangential acceleration of the rock?
4. What is the total acceleration of the rock?
5. What is the
Tangential component of the rock's velocity,
where
Length of string is L
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