A 85.0 cm diameter wheel accelerates uniformly from 220 rpm to 390 rpm in 7.0 s. How far will a point on the e

Question

A 85.0 cm diameter wheel accelerates uniformly from 220 rpm to 390 rpm in 7.0 s. How far will a point on the edge of the wheel have traveled in this time?

Answer 1

220 rpm=220*2*3.14/60 rad/sec
23.0 rad/sec

390 rpm=390*2*3.14/60 rad/sec

40.8 rad/sec

using
w=wi+α*t
40.8=23+α*7

solve for α

α=2.54


now use
th=wi*t+.5*α*t^2

th=23*7+.5*2.54*7^2
223 radians
d=th*r
d=223*85/2
9477 cm
or
94.8 m


j

Answer 2

A little help means you get to plug in the numbers. wi = 88.0 * 2 * pi (rad/s) wf = 316 * 2 * pi (rad/s) a = (wf - wi) / t theta = wi*t + 1/2*a*t^2 L = r * theta = 0.45 * theta plug and chug