1)If you increase the radius of revolution, how does the tension change (assuming all other variables remain the same)?
2) If you increase the revolving mass, how does the period of revolution change (assuming all other variables remain the same)?
3) If you increase the radius of revolution, how does the period of revolution change (assuming all other variables remain the same)?
4)If you increase the velocity of the revolving mass, how does the period of revolution change (assuming all other variables remain the same)?
Answer choices for all:
a) It increases.
b) It decreases.
c) It stays the same.
2) If you increase the revolving mass, how does the period of revolution change (assuming all other variables remain the same)?
3) If you increase the radius of revolution, how does the period of revolution change (assuming all other variables remain the same)?
4)If you increase the velocity of the revolving mass, how does the period of revolution change (assuming all other variables remain the same)?
Answer choices for all:
a) It increases.
b) It decreases.
c) It stays the same.
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For all circular motion, use this:
F/m = a = (v^2)/r
1) Tension is the force accelerating it inwards (aka turning it). Rearrange the equation for F in terms of r:
F = m(v^2)/r
If you increase the radius (r) you can see F gets smaller, since r is the denominator and you are dividing by a bigger number. Conceptually, a bigger radius means less sharp of turning so the force pulling it inwards would be less.
2) This one is confusing because they say all other variables remain the same. Looking at the equation again:
F/m=(v^2)/r
The mass in inscreased, so the velocity must decrease. If velocity decreases then the time it takes to go in one complete circle is longer.
3) Just like in #2, look at the equation and pay attention to v:
F/m=(v^2)/r
If the radius increases, the equation says the velocity would have to increase for the equation to still be mathematically correct (which it always is lol). Since v is faster, the time it takes to travel one revolution is now less.
4) This is a bad question. If you increase the velocity, you'd also have to increase the centripetal force 'F', otherwise it simply would not turn at that radius or with that mass. What they want you to see is that if the object is traveling in a circle faster, the time it takes to travel one revolution (the period) is less.
F/m = a = (v^2)/r
1) Tension is the force accelerating it inwards (aka turning it). Rearrange the equation for F in terms of r:
F = m(v^2)/r
If you increase the radius (r) you can see F gets smaller, since r is the denominator and you are dividing by a bigger number. Conceptually, a bigger radius means less sharp of turning so the force pulling it inwards would be less.
2) This one is confusing because they say all other variables remain the same. Looking at the equation again:
F/m=(v^2)/r
The mass in inscreased, so the velocity must decrease. If velocity decreases then the time it takes to go in one complete circle is longer.
3) Just like in #2, look at the equation and pay attention to v:
F/m=(v^2)/r
If the radius increases, the equation says the velocity would have to increase for the equation to still be mathematically correct (which it always is lol). Since v is faster, the time it takes to travel one revolution is now less.
4) This is a bad question. If you increase the velocity, you'd also have to increase the centripetal force 'F', otherwise it simply would not turn at that radius or with that mass. What they want you to see is that if the object is traveling in a circle faster, the time it takes to travel one revolution (the period) is less.
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1) A (just a guess here, though)
2) C (Mass is not a variable in p^2 = a^3)
3) A (Kepler's third law again)
4) B (Fairly straightforward; if the object is going faster it will take less time to make a revolution)
2) C (Mass is not a variable in p^2 = a^3)
3) A (Kepler's third law again)
4) B (Fairly straightforward; if the object is going faster it will take less time to make a revolution)