(a) Calculate the linear acceleration of a car, the 0.310-m radius tires of whic

Question

(a) Calculate the linear acceleration of a car, the 0.310-m radius tires of which have an angular acceleration of 13.5 rad/s2. Assume no slippage. 4.185 Correct: Your answer is correct. m/s2 (b) How many revolutions do the tires make in 2.50 s if they start from rest? 4.9 Incorrect: Your answer is incorrect. Consider the known variables to determine which rotational kinematic equation should be used here. rev (c) What is their final angular velocity? 25 Incorrect: Your answer is incorrect. Consider the known variables to determine which rotational kinematic equation should be used here. rad/s (d) What is the final velocity of the car? 7.5 Incorrect: Your answer is incorrect. Review the relationship between rotational and translational velocities. m/s

Explanation / Answer

(a) a = linear acceleration = to be determined
r = radius of each wheel = 0.310 m
= angular acceleration = 13.5 rad/s²

a = r* = 0.310*13.5 = 4.185 m/s^2

(b) = angular postion = to be determined
0 = initial angular velocity = 0 rad/s
= constant angular acceleration = 13.5 rad/s²

= 0 + 0.5t²
= 0.5t²
= 0.5(13.5 rad/s²)(2.50 s)²
= 42.1875 rad = 42.1875 rad / 2 rad = 6.71 revolutions Final Angular Position of Tires

(c) = final angular velocity = to be determined

² = (0)² + 2
² = 2
² = 2(13.5 rad/s²)(42.1875 rad)
² = 1139.0625 rad²/s²
= (1139.0625 rad²/s²)
= 33.75 rad/s Tires' Final Angular Velocity

(d) C = circumference of each wheel = 2r = 2(3.14159)(0.310 m) = 1.95 m
= 33.75 rad/s = 33.75 rad/s / 2 rad = 5.37 rev/s

v = 5.37 rev/s x 1.95 m/rev = 10.47 m/s Final Velocity of the Car

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.