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Engineering Question Essay Help Please
Hi,
I'm stuck on a question totally for a future exam and was wondering if anybody can help me out with this please.
Thaks very much in advance.
Chris
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a gear of radius 0.4m and a gear of radius 1.2m are connected by a belt. if the smaller gear is rotating with an angular velocity of 10 rad/s, find the angular velocity of the larger gear.
here is the formula: v = rw
a. what can be said about the linear velocity of a point on the edge of gear 1 and the velocity of the belt?
b. because it is the movement of the belt that causes gear 2 to turn, what can be said about the linear velocity of a point on the outside of gear 2?
c. using the linear velocity of the points on the outside of gear 2, found in step b, and the radius of gear 2, find the gear's angular velocity.
d. what is the relationship between the angular velocity of gear1 and the angular velocity of gear 2?
I'm stuck on a question totally for a future exam and was wondering if anybody can help me out with this please.
Thaks very much in advance.
Chris
----------------------------------------------
a gear of radius 0.4m and a gear of radius 1.2m are connected by a belt. if the smaller gear is rotating with an angular velocity of 10 rad/s, find the angular velocity of the larger gear.
here is the formula: v = rw
a. what can be said about the linear velocity of a point on the edge of gear 1 and the velocity of the belt?
b. because it is the movement of the belt that causes gear 2 to turn, what can be said about the linear velocity of a point on the outside of gear 2?
c. using the linear velocity of the points on the outside of gear 2, found in step b, and the radius of gear 2, find the gear's angular velocity.
d. what is the relationship between the angular velocity of gear1 and the angular velocity of gear 2?
Answers
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The radius of the larger gear is 3 times that of the smaller.
Assuming the belt does not slip, the belt velocity, v, is constant. Therefore, the angular velocity of the larger gear must be 1/3 of that of the smaller gear - i.e. 3.333 rad/s.
a. again, assuming no belt slip, the belt velocity must be equal to the velocity of the edge of the gear.
b. similarly, the linear velocity of the edge of gear 2 is equal to the belt velocity.
c. 3.333 rad/s
d. as explained, using w for omega, w1 = 3 x w2.
One point, why are gears connected by a belt ?
Assuming the belt does not slip, the belt velocity, v, is constant. Therefore, the angular velocity of the larger gear must be 1/3 of that of the smaller gear - i.e. 3.333 rad/s.
a. again, assuming no belt slip, the belt velocity must be equal to the velocity of the edge of the gear.
b. similarly, the linear velocity of the edge of gear 2 is equal to the belt velocity.
c. 3.333 rad/s
d. as explained, using w for omega, w1 = 3 x w2.
One point, why are gears connected by a belt ?
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