Linear and Angular Velocity Worksheet w/Answers

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4.
Ship's Propeller Problem
The propellers on an
average freighter have a radius of 4 ft (Figure
4-4e). At full speed ahead, the propellers turn at
150-rpm.
a.
What is the angular velocity in radians per
minute at the tip of the blades? at the center
of the propeller?
What is the linear velocity in feet per minute
at the tip of the blades? at the center of the
propeller?
b.
Lawn Mower Blade Problem
In order for a
lawn mower blade (Figure 4-4f) to cut grass, it
must strike the grass with a speed of at least
900 in/s.
a. If the innermost part of the cutting edge is
6 in. from the center of the blade, how many
radians per second must the blade turn? How
many revolutions per minute is this?
b. The blade has a diameter of 19 in. If the outermost tip of the blade hits a rock while turning as in part (a), how fast could the rock be
hurled from the mower?
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19"
5.
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',}gure 4-4e
2.
Ferris WheeL Problem
Dan Druff and Ella Funt
are riding on a Ferris wheel. Dan observes that it
takes 20 s to make a complete revolution. Their
seat is 25 ft from the axle· of the wheel.
a.
b.
3.
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_
.\
Lawn Mower Cord Problem
Yank Hardy pulls
the cord on his power mower. In order for the
engine to start, the pulley must turn at 180 revolutions per minute. The pulley has a radius of
0.2 ft (Figure 4-4g).
a. How many radians per second must the pulley turn?
b, How fast must Yank pull the cord to start the
mower?
c. When Yank pulls this hard, what is the angular velocity of the center of the pulley?
What is their angular velocity in revolutions
per minute? degrees per minute? radians per
minute?
What is their linear velocity?
David and Goliath Problem
David puts a rock
in his sling and starts whirling it around. He realizes that in order for the rock to reach Goliath, it
must leave the sling at a speed of 60 ftls. So he
swings the sling in a circular path of radius 4 ft.
What must the angular velocity be in order for
David to achieve his objective?
6. Cockroach Problem
A cockroach is sitting
4 em from the center of a Lazy Susan. Unaware
of its presence, Phoebe Small spins the Lazy Susan through an angle of 120°.
a. Through how many radians did the roach
turn?
b. What distance did it travel?
c. If Phoebe turned the Lazy Susan 1200 in
4 second, what was the roach's angular
velocity?
d. What was its linear velocity?
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