The tips of the blades in a food blender are moving with a speed of 23 m/s in a circle that
has a radius of 0.058 m. How much time does it take for the blades to make one
A stone has a mass of 2.0 10-3 kg and is wedged into the tread of an automobile tire, as
the drawing shows. The coefficient of static friction between the stone and each side of
the tread channel is 0.88. When the tire surface is rotating at 14 m/s, the stone flies out
of the tread. The magnitude FN of the normal force that each side of the tread channel
exerts on the stone is 1.8 N. Assume that only static friction supplies the centripetal
force, and determine the radius r of the tire.
A "swing" ride at a carnival consists of chairs that are swung in a circle by 12.0-m cables
attached to a vertical rotating pole, as the drawing shows. ( = 62.0°) Suppose the total
mass of a chair and its occupant is 198 kg.
(a) Determine the tension in the cable attached to the chair.
(b) Find the speed of the chair.
At what angle should a curve of radius 190 m be banked, so cars can travel safely at 32
m/s without relying on friction?
A curve of radius 180 m is banked at an angle of 18°. At what speed can it be negotiated
under icy conditions where friction is negligible?
On a banked race track, the smallest circular path on which cars can move has a radius r1 =
104 m, while the largest has a radius r2 = 161 m, as the drawing illustrates. The height of
the outer wall is 18 m.
(a) Find the smallest speed at which cars can move on this track without relying on
(b) Find the largest speed at which cars can move on this track without relying on friction.
A motorcycle has a constant speed of 21.0 m/s as it passes over the top of a hill whose
radius of curvature is 142 m. The mass of the motorcycle and driver is 338 kg. Find the
(a) the centripetal force and
(b) the normal force that acts on the cycle.
A 2100 kg demolition ball swings at the end of a 15 m cable on the arc of a vertical circle.
At the lowest point of the swing, the ball is moving at a speed of 6.4 m/s. Determine the
tension in the cable. (Hint: The tension serves the same purpose as the normal force at
point 1 in Figure 5.21.)
A train is rounding a circular curve whose radius is 2.00 102 m. At one instant, the train
has an angular acceleration of 1.50 10-3 rad/s2 and an angular speed of 0.0100 rad/s.
(a) Find the magnitude of the total acceleration (centripetal plus tangential) of the train.
(b) Determine the angle of the total acceleration relative to the radial direction.
The shaft of a pump starts from rest and has an angular acceleration of 6.00 rad/s2 for
10.0 s. At the end of this interval, what is
(a) the shaft's angular speed and
(b) the angle through which the shaft has turned?
A certain CD has a playing time of 64 minutes. When the music starts, the CD is rotating
at an angular speed of 4.8 102 revolutions per minute (rpm). At the end of the music, the
CD is rotating at 2.1 102 rpm. Find the magnitude of the average angular acceleration of
the CD. Express your answer in rad/s2.
The angular speed of the rotor in a centrifuge increases from 500 to 1500 rad/s in a time
of 5.00 s.
(a) Obtain the angle through which the rotor turns.
(b) What is the angular acceleration?
A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction.
The wheel has an angular acceleration of -4.60 rad/s2. Because of this acceleration, the
angular velocity of the wheel changes from its initial value to a final value of -24.0 rad/s.
While this change occurs, the angular displacement of the wheel is zero. (Note the
similarity to that of a ball being thrown vertically upward, coming to a momentary halt, and
then falling downward to its initial position.) Find the time required for the change in the
angular velocity to occur.
The angular speed of an automobile engine is increased at a constant rate from 1300
rev/min to 4000 rev/min in 11 s.
(a) What is its angular acceleration in revolutions per minute-squared?
(b) How many revolutions does the engine make during this 11 s interval?
A disk rotates about its central axis starting from rest and accelerates with constant
angular acceleration. At one time it is rotating at 10 rev/s. Then 70 revolutions later, its
angular speed is 18 rev/s.
(a) Calculate the angular acceleration.
(b) Calculate the time required to complete the 70 revolutions mentioned.
(c) Calculate the time required to attain the 10 rev/s angular speed.
(d) Calculate the number of revolutions from rest until the time the disk attained the 10
rev/s angular speed.
An air puck of mass 0.037 kg is tied to a string and allowed to revolve in a circle of radius
0.9 m on a frictionless horizontal surface. The other end of the string passes through a
hole in the center of the surface, and a mass of 0.4 kg is tied to it, as shown in Figure 7-
19. The suspended mass remains in equilibrium while the puck revolves on the surface.
(a) What is the magnitude of the force that maintains circular motion acting on the puck?
(b) What is the linear speed of the puck?
In a popular amusement-park ride, a cylinder of radius 4.00 m is set in rotation at an
angular speed of 3.00 rad/s, as shown in Figure 7-20. The floor then drops away, leaving
the riders suspended against the wall in a vertical position. What minimum coefficient of
friction between a rider's clothing and the wall of the cylinder is needed to keep the rider
from slipping? (Hint: Recall that Fs = µsFn, where the normal force is the force that
maintains circular motion.)