Concept explainers
Repeat Problem 87, now generalizing to the case where not only the speed but also the radius may be changing.
87. In dealing with nonuniform circular motion, as shown in Fig. 3.23, we should write Equation 3.16 as ar = v2/r, to show that this is only the radial component of the acceleration. Recognizing that v is the object’s speed, which changes only in the presence of tangential acceleration, differentiate this equation with respect to time to find a relation between the magnitude of the tangential acceleration and the rate of change of the magnitude of the radial acceleration. Assume the radius stays constant.
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Essential University Physics (3rd Edition)
Additional Science Textbook Solutions
Cosmic Perspective Fundamentals
Physics (5th Edition)
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Conceptual Integrated Science
Introduction to Electrodynamics
- From a tower of height yo a particle is projected vertically up with a velocity vo in free space (gravity free). The acceleration of particle at an instant is given as ā = k (v ×Ā), where v is instantaneous velocity vector and A is given as A = (-k), where y is the H y vertical coordinate of particle at that instant. (Take origin as foot of the tower) Answer the following questions. D 14. The speed of particle as a function of time will be (A) vo + kt (C) Vo-y/t 15. (B) vo+ (y/t)-(1/2)at (D) Vo The maximum height attain by the particle will be (A) y = Yo(1+evo/Kc) (C) y = Yo (1-evo/kc) (B) y = Yo(1+e */v) (D) y Yo (1-e-c/vo) t Yo (0, 0)arrow_forwardA ball is traveling at a constant speed (v) of 40.0 m/s in a circle with a radius (r) of 6.0 m. (Hint: The circumference C = 2πr) The centripetal acceleration is ZERO a. False b. True The total distance traveled by the ball is: How long in time does it take for the ball complete one circle? The displacement traveled by the ball is: The average speed of the ball is: The average velocity of the ball is:arrow_forwardA car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in above figure. The length of the arc ABC is 235m, and the car completes the turn in 36.0s. (a) What is the acceleration when the car is at B located at an angle of 35.08? Express your answer in terms of the unit vectors i^ and j . Determine (b) the cars average speed and (c) its average acceleration during the 36.0s interval.arrow_forward
- (The complete question is in the picture) While being chased, Percy Jackson spotted the Poseidon’s pearltraversing around the roulette wheel in circular trajectory. The acceleration of the pearl ispurely perpendicular to its trajectory, and has a value of 1.25 [m/s2]. If the diameter of thecircular path is 40.0 [cm], what is the magnitude of the velocity of the pearl?A. 0.500 [m/s]B. 0.707 [m/s]C. 5.00 [m/s]D. 7.07 [m/s]arrow_forwardQuestion 6: A particle is moving in a circular path of radius R. At some in- stant, its acceleration a makes angle 0 with the horizontal as shown in Figure 2. At that instant, what is the speed of the particle? Figure 2 Select one: VaR cos 0 VaRtan 0 VaRsin 0 aR cot 0 aRsin? 0arrow_forwardThe radius of the earth is R. At what distance above the earth's surface, in terms of R , is the acceleration due to gravity = 2.5 m/s2 ? At approximately (answer) × R above the earth’s surface.arrow_forward
- Problem 2: In baseball the pitcher will throw baseballs horizontally and to account for gravity, the pitcher will stand upon a raised mound. Take the pitcher's release point to be 1.2m above the ground and they will hit a spot 0.7m above the ground at a distance 20m away. a) Draw ST vs t, sy VS t, Uz VS t,, Vy vs t, a vs t,, and ay vs t, graphs of the baseball's motion b) from Kinematic Equations on the first page Prove that the velocity needed is = 9(Asz)² V24sy symbolically by starting c) If the pitcher was playing on Mars (g = 3.7m/s, negligible air resistance) how fast would they have to pitch?arrow_forwardA rotating fan completes 1200 revolutions every minute. Consider the tip of a blade, at a radius of 0.15 m. (a) Through what distance does the tip move in one revolution? What are (b) the tip’s speed and (c) the magnitude of its acceleration? (d) What is the period of the motion?arrow_forwardA hawk flies at 12.0 m/s in a horizontal circle of radius 12.0 m. Now suppose it flaps its wings harder and increases its circular speed at the rate of 1.20 m/s2 while staying in the same circular path. What is the magnitude of its acceleration, and in what direction is the acceleration vector?arrow_forward
- 2 = 2500 cos 20 13. For a short time, the jet plane moves along a path in the shape of a lemniscate, r² = (2500cos 26) km². At the instant 0=30°, the radar tracking device is rotating at O =5(103) rad/s with ö=2(103) rad/s². Determine the components of the velocity and acceleration of the plane at this instant, a) in Cartesian Coordinates, b) in Normal and Tangential Coordinates, c) in Polar Coordinates. d) Also calculate the radius of curvature at the same instant.arrow_forwardTo anticipate the dip and the hump in the road, the driver of a car applies his brakes to produce a uniform deceleration. His speed is 100kph at the bottom A of the dip and 50 kph at the top C of the hump. The length of the road from A to Cis 120m. The radius of curvature of the hump at C is 150m. The total acceleration at A is 3 m/s^2. Compute the total acceleration in m/s^2 at C. 60 m В 60 m A A) 3.69 2.66 2.73 D) 3.08 E) 2.96arrow_forwardOn a dare from a friend, you decide to try to jump a canyon using your bicycle as shown in the figure below. We will define a successful jump as one that allows you to just make it to the edge of the canyon on the far side. Ꮎ Yramp Calculate all the following: A custom ramp has been constructed for you which is yo = 29.6 meters high and is tipped an an angle of 0 = 44.7 degrees. The canyon has a width of Xcanyon 106.8 meters. Xcanyon The initial velocity, vo, of your bike? meters/second The time spent flying through the air second guessing your judgement? secondsarrow_forward
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University