HW 8

Homework 8 Problems: Rotational Motion
1. The rotor on a helicopter turns at an angular speed of
revolutions per minute.
a. [3 points] Express this angular speed in radians per second.
b. [4 points] If the rotor has a radius of 2.00 m, determine the tangential speed. What
arc length does the tip of the blade trace out in
?
c. [3 points] Suppose that the pilot opens the throttle, and the angular speed of the
blade increases while rotating twenty-six times in 3.60 s. Calculate the average
angular speed during this time.
2. A pail of water is rotated in a vertical circle of radius 1.00 m.
a. [3 points] What two external forces act on the water in the pail? Which of the two
forces is most important in causing the water to move in a circle?
b. [4 points] What is the pail’s minimum speed at the top of the circle if no water is
to spill out?
c. [3 points] If the pail with the speed found in part (b) were to suddenly disappear at
the top of the circle, describe the subsequent motion of the water.
3. An air puck of mass
is tied to a string and allowed to revolve in a circle
of radius
on a horizontal, frictionless table. The other end of the string
passes through a small hole in the center of the table, and a block of mass
tied to it, as shown below. The suspended object remains in equilibrium while the puck
on the tabletop revolves.
a. [2 points] Draw a free body diagram for both objects
b. [4 points] Determine the tension in the string.
c. [4 points] Determine the speed of the puck.
4. A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of
magnitude 1.75 m/s2 after its brakes are applied.
a. [7 points] How many revolutions does each tire make before the car comes to a
stop, assuming the car does not skid and the tires have radii of 0.330 m?
b. [3 points] What is the angular speed of the wheels when the car has traveled half
the total distance?
5. One end of a cord is fixed and a small 0.500-kg object is attached to the other end, where
it swings in a section of a vertical circle of radius 2.00 m, as shown below. When θ =
20.0°, the speed of the object is 8.00 m/s.
a. [4 points] Find the tension in the string,
b. [3 points] Find the tangential and radial components of acceleration. Find the total
acceleration.
c. [3 points] Is your answer changed if the object is swinging down toward its lowest
point instead of swinging up? Explain your answer.
Bonus [7 points]: A car rounds a banked curve where the radius of curvature of the road is
, the banking angle is
, and the coefficient of static friction is
(slippery conditions). (a) Determine the range of speeds the car can have without slipping up or
down the road. (b) Discuss conceptually what would happen to your answers to (a) if either
increases or increases.