Angular velocity is dθ/dt. It's a measure of how fast something is revolving in a circular orbit, independent of how big that orbit is. If you are still confused, post some questions where you were unsure of which equation to use.
Here is the necessary concept I had forgotten completely. Indeed, Vt decreases as the orbit size decreases. So in Merry-go around example, as the child moves to the center,
r decreases, but Vt decreases as well. However,
w doesn't change cause dθ/dt doesn't change.
BR CH Force Motion Gravitation Passage IV
#23 If a person starts at the rim of the space station and moves radially towards the central axis in an elevator, what happen to the normal force felt by that person?
Answer: N = mac = w^2r so, N decreases.
Just as the merrygoaround example
BR CH Equilibrium and Momentum Passage X
#68 As the crane rotates, it increases its speed. What effect will this have on the tension in the cable and on the angle the cable makes with the vertical?
- Previously, this I could answer just by imagining, but was not able to answer in an intuitive way, and drawing diagram and playing with equations took too much time.
- Let's see whether my understanding is correct. Increasing its speed in this question means increasing its angular velocity, cause it's rotating faster. so this increases the centripetal force which is tension?
#69 As the crane rotates, and
linearly increases its speed, what can be said about the torque aciting on the load?
How could a crane linearly increase its speed?? It's saying that it won't change the angular acceleration, so no change in torque as well.
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