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Suppose you have an incline plane 120 cm long and inclined at 7.5 deg. Suppose you have a rotator (you aren't told if it's a sphere, disk, ring ... or something else...); the rotator is released from rest, rolls without slipping, and attains a center of mass velocity of 150 cm/s at the end of the incline. Leť's say this object has a mass of 50 grams and a radius of 2 cm. Whať's its moment of inertia, I, in grams x centimeters ^2? (since you don't know what sort of object this is, you have no way to automatically calculate its I, you need to use conservation of energy to figure out its I thru heavy use of algebra, good luck). What sort of rotator is this the closest to? (to answer THIS question, examine the value you get for I and compare it to the value you get if you simply do mR^2; take the ratio of I to mR^2 and compare this to the coefficients of various rotators which are typically of the form (coefficient) x mR^2). Hint – to use conservation of energy correctly, you need to factor the rotational kinetic energy, K-rot = (1/2) I (omega)^2 where (omega) is the angular velocity; you need to recall that the no slip condition is (center of mass velocity) = (radius) x (omega)

Suppose you have an incline plane 120 cm long and inclined at 7.5 deg. Suppose you have a rotator (you aren't told if it's a sphere, disk, ring ... or something else...); the rotator is released from rest, rolls without slipping, and attains a center of mass velocity of 150 cm/s at the end of the incline. Leť's say this object has a mass of 50 grams and a radius of 2 cm. Whať's its moment of inertia, I, in grams x centimeters ^2? (since you don't know what sort of object this is, you have no way to automatically calculate its I, you need to use conservation of energy to figure out its I thru heavy use of algebra, good luck). What sort of rotator is this the closest to? (to answer THIS question, examine the value you get for I and compare it to the value you get if you simply do mR^2; take the ratio of I to mR^2 and compare this to the coefficients of various rotators which are typically of the form (coefficient) x mR^2). Hint – to use conservation of energy correctly, you need to factor the rotational kinetic energy, K-rot = (1/2) I (omega)^2 where (omega) is the angular velocity; you need to recall that the no slip condition is (center of mass velocity) = (radius) x (omega)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Suppose you have an incline plane 120 cm long and inclined at 7.5 deg. Suppose you have a rotator (you aren't told if it's a sphere, disk, ring or something else...); the rotator is released ... from rest, rolls without slipping, and attains a center of mass velocity of 150 cm/s at the end of the incline. Leť's say this object has a mass of 50 grams and a radius of 2 cm. Whať's its moment of inertia, I, in grams x centimeters ^2? (since you don't know what sort of object this is, you have no way to automatically calculate its I, you need to use conservation of energy to figure out its I thru heavy use of algebra, good luck). What sort of rotator is this the closest to? (to answer THIS question, examine the value you get for I and compare it to the value you get if you simply do mR^2; take the ratio of I to mR^2 and compare this to the coefficients of various rotators which are typically of the form (coefficient) x mR^2). Hint – to use conservation of energy correctly, you need to factor the rotational kinetic energy, K-rot = (1/2) I (omega)^2 where (omega) is the angular velocity; you need to recall that the no slip condition is (center of mass velocity) = (radius) x (omega)
Transcribed Image Text:Suppose you have an incline plane 120 cm long and inclined at 7.5 deg. Suppose you have a rotator (you aren't told if it's a sphere, disk, ring or something else...); the rotator is released ... from rest, rolls without slipping, and attains a center of mass velocity of 150 cm/s at the end of the incline. Leť's say this object has a mass of 50 grams and a radius of 2 cm. Whať's its moment of inertia, I, in grams x centimeters ^2? (since you don't know what sort of object this is, you have no way to automatically calculate its I, you need to use conservation of energy to figure out its I thru heavy use of algebra, good luck). What sort of rotator is this the closest to? (to answer THIS question, examine the value you get for I and compare it to the value you get if you simply do mR^2; take the ratio of I to mR^2 and compare this to the coefficients of various rotators which are typically of the form (coefficient) x mR^2). Hint – to use conservation of energy correctly, you need to factor the rotational kinetic energy, K-rot = (1/2) I (omega)^2 where (omega) is the angular velocity; you need to recall that the no slip condition is (center of mass velocity) = (radius) x (omega)
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