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A block of mass m is placed on a frictionless horizontal turntable at a distance r from the center. The turntable is rotating with a constant angular speed ฯ‰. The block is held in place by a string attached to the center of the turntable. Draw and label all the forces acting on the block before the string is cut.

N (Normal Force) pointing upward, mg (Gravitational Force) pointing downward, T (Tension) pointing toward the center.

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A block of mass m is placed on a frictionless horizontal turntable at a distance r from the center. The turntable is rotating with a constant angular speed ฯ‰. The block is held in place by a string attached to the center of the turntable. Draw and label all the forces acting on the block before the string is cut.
N (Normal Force) pointing upward, mg (Gravitational Force) pointing downward, T (Tension) pointing toward the center.
What are the key differences between centripetal and tangential acceleration?
Centripetal: Changes direction of velocity, points towards the center | Tangential: Changes speed, acts tangent to the path.
Compare period and frequency.
Period: Time for one revolution (seconds) | Frequency: Revolutions per second (Hertz). They are inversely related.
How do you calculate the magnitude of centripetal acceleration?
Use the formula: $a_{c} = \frac{v^2}{r}$, where v is tangential speed and r is the radius.
How do you find the minimum speed required to stay on the track at the top of a vertical loop?
Use the formula: $v = \sqrt{gr}$, where g is the acceleration due to gravity and r is the radius of the loop.
How do you calculate the period (T) using speed and radius?
Use the formula: $T = \frac{2 \pi r}{v}$, where r is the radius and v is the speed.
How do you calculate the net acceleration in circular motion?
Find the vector sum of centripetal and tangential accelerations. Remember they are perpendicular.
How do you calculate the relationship between period and frequency?
Use the formula: $T = \frac{1}{f}$