Ch 04: Kinematics in Two Dimensions
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Problem 4
The cannon in FIGURE CP4.83 fires a projectile at launch angle θ with respect to the slope, which is at angle Φ. Find the launch angle that maximizes d. Hint: Choosing the proper coordinate system is essential. There are two options.Problem 4
You have a remot-controlled car that has been programmed to have velocity v = (3ti + 2t^2j) m/s, where t is in s. At t = 0 s, the car is at r0 = (3.0i + 2.0j) m. What are the car's (a) position vectorProblem 4
The radius of the earth's very nearly circular orbit around the sun is 1.5 x 10^11m. Find the magnitude of the earth's (a) velocityProblem 4
The radius of the earth's very nearly circular orbit around the sun is 1.5 x 10^11m. Find the magnitude of the earth's (b) angular velocityProblem 4
Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is 6.37 x 10⁶ m, and the altitude of a geosynchronous orbit is 3.58 x 10⁷ m (≈ 22,000 miles). What are (a) the speed and (b) the magnitude of the acceleration of a satellite in a geosynchronous orbit?Problem 4
FIGURE EX4.23 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?
Problem 4
FIGURE EX4.24 shows the angular-position-versus-time graph for a particle moving in a circle. What is the particle's angular velocity at (b) t = 4s
Problem 4
The earth's radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles. The flight from Kampala to Singapore takes 9.0 hours. What is the plane's angular velocity with respect to the earth's surface? Give your answer in degrees/h.Problem 4
As the earth rotates, what is the speed of (a) a physics student in Miami, Florida, at latitude 26 degreesProblem 4
A typical laboratory centrifuge rotates at 4000 rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. a. What is the acceleration at the end of a test tube that is 10 cm from the axis of rotation?Problem 4
A Ferris wheel of radius R speeds up with angular acceleration starting from rest. Find expressions for the (a) velocity and (b) centripetal acceleration of a rider after the Ferris wheel has rotated through angle ∆θ.Problem 4
A 6.0-cm-diameter gear rotates with angular velocity ω = ( 20 ─ ½ t² ) rad/s where t is in seconds. At t = 4.0 s, what are: a. The gear's angular acceleration?Problem 4
A 6.0-cm-diameter gear rotates with angular velocity ω = ( 20 ─ ½ t² ) rad/s where t is in seconds. At t = 4.0 s, what are: b. The tangential acceleration of a tooth on the gear?Problem 4
A painted tooth on a spinning gear has angular position θ = (6.0 rad/s⁴)t⁴. What is the tooth's angular acceleration at the end of 10 revolutions?Problem 4
The angular velocity of a process control motor is ω = ( 20 ─ ½ t² ) rad/s, where t is in seconds. b. Through what angle does the motor turn between t = 0 s and the instant at which it reverses direction?Problem 4
Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decelerates to a halt in 2.0 s. How many revolutions does it make?Problem 4
A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s. (b) How many revolutions does the merry-go-round make as it stops?Problem 4
Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the pebble's speed and acceleration?Problem 4
A computer hard disk 8.0 cm in diameter is initially at rest. A small dot is painted on the edge of the disk. The disk accelerates at 600 rad/s² for ½s, then coasts at a steady angular velocity for another ½s. b. Through how many revolutions has the disk turned?Problem 4
FIGURE EX4.36 shows the angular velocity graph of the crankshaft in a car. What is the crankshaft's angular acceleration at (b) t = 3s
Problem 4
The angular velocity of a spinning gyroscope is measured every 0.5 s. The results and the best-fit line from a spreadsheet are shown in FIGURE P4.63.
a. What is the gyroscope's initial angular velocity, at t = 0 s?
Problem 4
A 25 g steel ball is attached to the top of a 24-cm-diameter vertical wheel. Starting from rest, the wheel accelerates at 470 rad/s². The ball is released after ¾ of a revolution. How high does it go above the center of the wheel?Problem 4
The angular velocity of a process control motor is ω = ( 20 ─ ½ t² ) rad/s, where t is in seconds. a. At what time does the motor reverse direction?Problem 4
A particle moving in the xy-plane has velocity v = (2ti + (3-t^2)j) m/s, where t is in s. What is the particle's acceleration vector at t = 4s?Problem 4
A particle's trajectory is described by x = (1/2t^2 - 2t^2)m and y = (1/2 t^2-2t)m, where t is in s. (a) What are the particle's position and speed at t = 0 s and t = 4s?Problem 4
Susan, driving north at 60 mph, and Trent, driving east at 45 mph, are approaching an intersection. What is Trent's speed relative to Susan's reference frame?Problem 4
Flywheels—rapidly rotating disks—are widely used in industry for storing energy. They are spun up slowly when extra energy is available, then decelerate quickly when needed to supply a boost of energy. A 20-cm-diameter rotor made of advanced materials can spin at 100,000 rpm. a. What is the speed of a point on the rim of this rotor?Problem 4
Flywheels—rapidly rotating disks—are widely used in industry for storing energy. They are spun up slowly when extra energy is available, then decelerate quickly when needed to supply a boost of energy. A 20-cm-diameter rotor made of advanced materials can spin at 100,000 rpm. b. Suppose the rotor's angular velocity decreases by 40% over 30 s as it supplies energy. What is the magnitude of the rotor's angular acceleration? Assume that the angular acceleration is constant.Problem 4
A rocket-powered hockey puck moves on a horizontal frictionless table. Figure EX4.7 shows graphs of and , the x- and y-components of the puck's velocity. The puck starts at the origin. What is the magnitude of the puck's acceleration at t = 5s?
Problem 4
(a) Complete the motion diagram by adding acceleration vectors.
