Homework
Section 1
Name_________________________________
1. A baseball pitcher brings his arm forward during a pitch, rotating the forearm about the elbow. If the velocity of the
ball in the pitcher's hand is 25.5 m/s and the ball is 0.250 m from the elbow joint, what is the angular velocity of the
forearm? In rad/s
2. In lacrosse, a ball is thrown from a net on the end of a stick by rotating the stick and forearm about the elbow. If the
angular velocity of the ball about the elbow joint is 20.0 rad/s and the ball is 1.05 m from the elbow joint, what is the
velocity of the ball? In m/s
3. A truck with 0.250 m radius tires travels at 24.0 m/s. At how many radians per second are the tires rotating? What is
this in rpm? Find both rad/s and rpm (rotations per minute) Two answers are needed
4. An ordinary workshop grindstone has a radius of 8.50 cm and rotates at 6000 rpm.
(a) Calculate the centripetal acceleration at its edge in m/s2 and convert it to multiples of g.
(b) What is the linear speed of a point on its edge? In m/s
5. At takeoff a commercial jet has a 50.0 m/s speed. Its tires have a diameter of 0.850 m.
(a) At how many rpm are the tires rotating? In rpm
(b) What is the centripetal acceleration at the edge of the tire? In m/s2
(c) With what force must a determined 10-15 kg bacterium cling to the rim? In N
(d) Take the ratio of this force to the bacterium's weight.
(force from part (c) / bacterium's weight)
6.
(a) A 15.0 kg child is riding a playground merry-go-round that is rotating at 45.0 rpm. What centripetal force must she
exert to stay on if she is 1.50 m from its center?
(b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rpm if she
is9.00 m from its center?
(c) Compare each force with her weight.
(force from part (a) / weight)
(force from part (b) / weight)
7. A certain car has a minimum turning radius of 8.2 m . If the coefficient of static friction between the tires and road is
μ=0.13, what is the maximum speed the car can have without skidding on an unbanked road if the steering wheel is
turned fully to the right? In m/s
8. In what direction is the force acting on the earth as it orbits sun? Select One
Toward the center of the galaxy.
Clockwise.
Counter clockwise.
Toward the center of the earth.
Toward the center of the sun.
Section 2
1. Consider a ball on a fixed-length string being whirled in a
vertical circular path as shown in the diagram below.
(a) When the ball is at location A what is the direction of the
velocity vector?
(b) When the ball is at location B what is the direction of the
velocity vector?
(c) When the ball is at location C what is the direction of the
net FORCE vector?
2. A rigid wheel of radius r rotates about an axis through the center and perpendicular to the plane of the wheel.
Consider three points A, B, and C on the wheel, indicated by the small red circles. Location A is on the rim, locations B
and C are on two different spokes of the wheel at a distance r/2 from the center. Consider the rotation of the wheel
during a certain interval of time Δt.
(a)
Which of the following is true regarding the angular velocity? Select One.
1)All three points have the same angular velocity as all three points have the same
angular displacement θ in the same time interval Δt.
2)Points B and C will have half the angular velocity of point A as they are at half the
distance from the center of the wheel compared to A.
3)Points B and C will have twice the angular velocity of point A as they are at half the
distance from the center of the wheel compared to A.
(b) Which of the following is true regarding the tangential speed? Select one:
1)All three points have the same tangential speed as all three points have the same angular displacement θ in
the same time interval Δt.
2)Point A has a greater tangential speed as it is further away from the center of the wheel.
3)Points B and C will have a greater tangential speed as they are closer to the center.
(c) Which of the following is true regarding centripetal acceleration? (Select all that apply.)
1)All three points have the same centripetal acceleration as all three points have the same angular displacement
θ in the same time interval Δt.
2)Points B and C will have half the centripetal acceleration of point A as they are at half the distance from the
center of the wheel compared to A.
3)Points B and C will have twice the centripetal acceleration of point A as they are at half the distance from the
center of the wheel compared to A.
3. You whirl a stone in a horizontal circle in such a way that the stone is in uniform circular motion. Which of the
following is true for this situation? (Select all that apply.)
-The stone is moving with constant velocity.
-The magnitude of the stone's velocity does not change.
-The change in direction of the stone's motion is due to the centripetal force acting on the stone.
-The stone's speed is constant.
-The direction of the stone's velocity changes as it moves around the circle.
4. You whirl a ball tied to the end of the rope in a horizontal circle at constant speed, as shown in the diagram below.
Use the direction rosette to answer the following questions.
(a) What is the direction of the centripetal force acting
on the ball when it is at location A?
(b) If the string breaks when the ball is at location A, in
what direction will the ball move?
6. You and your family take a road trip on a long holiday weekend. In a certain section of the trip where the road is
particularly uneven, the car goes over a bump that is curved downward with a radius of 17.0 m. See diagram below. The
mass of the car and its passengers is 1900 kg.
(a) When the car is at the highest point of the bump its speed is 7.05 m/s.
Determine the magnitude and direction of the force exerted by the road on
the car at this highest point.
Magnitude __________________N
Direction ____________________
(b) If the speed at the highest point is above a certain maximum value the car will lose contact with the road. Calculate
this maximum speed. _______________m/s
7. Modern roller coasters have vertical loops like the one shown in Figure 8.32. The radius of curvature is smaller at the
top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due
to gravity, keeping the passengers pressed firmly into their seats.
(a) What is the speed of the roller coaster at the top of the loop if the radius of
curvature there is 13.0 m and the downward acceleration of the car is 1.50 g?
_________________m/s
(b) How high above the top of the loop must the roller coaster start from rest,
assuming negligible friction? ______________m
(c) If it actually starts 5.00 m higher than your answer to the previous part, how
much energy did it lose to friction? Its mass is 1600 kg. ________________J