226k views
3 votes
A wheel 30 cm in diameter accelerates uniformly from 245 rpm to 380 rpm in 6.1 s . Part A How far will a point on the edge of the wheel have traveled in this time

User Ladaghini
by
8.0k points

1 Answer

5 votes

Answer:

A point on the edge of the wheel will travel 199.563 radians at the given time.

Step-by-step explanation:

Given;

initial angular velocity of the wheel;
\omega _i = 245 \ rev/\min = 245\ (rev)/(\min) * (2\pi)/(1\ rev) * (1 \ \min)/(60 \ s) = 25.66 \ rad/s

final angular velocity of the wheel;


\omega _f = 380 \ rev/\min = 380 \ (rev)/(\min) * (2\pi)/(1\ rev) * (1 \ \min)/(60 \ s) = 39.80 \ rad/s

radius of the wheel, d/2 = (30 cm ) / 2 = 15 cm = 0.15 m

time of motion, t = 6.1 s

The angular distance traveled by the edge of the wheel is calculated as;


\theta = ((\omega_f + \omega_i)/(2) )t\\\\\theta = ((39.8 + 25.66)/(2) )* 6.1\\\\\theta = 199.653 \ radian

Therefore, a point on the edge of the wheel will travel 199.563 radians at the given time.

User Hochopeper
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.