Question

A wheel of a car is measured to rotate 200 revolutions in 24 seconds. Calculate the following.

i. The angle turned in radians?

θ =degree * 2π/360=
θ=200 *2π/360
θ=3.49

ii. The angular velocity in rad/s

ω=θxt
ω=3.94/24
ω=0.145 rad/s

If the diameter of the wheel is 0.5 m

iii, what is the linear velocity of the car

v=ωxr
v=0.145 x 0.5
v=0.0725/s

Answer 1

i. incorrect.
The angle turned in <b>radians</b>?
note
(2π/360) is the conversion factor from degrees to radians.
use
1 revolution = 2π radians

For example,
5 revolutions equals (5*2π)=10π radians.


ii. incorrect
error inherited from (i)

iii. incorrect
error inherited from (ii)

Answer 2

(i) one revolution is 2πradians, so
θ = 200*2π = 400π radians

(ii)angular velocity is measured in radians/second, so

ω = θ/t = 400πrad/24s = 50π/3 rad/s

(iii)v = rωt
v = 1/4 * 50π/3 * 24 = 100π m/s

or, since the circumference is πd = π/2 meters per revolution,

v = 200rev/s * π/2 m/rev = 100π m/s

Looks like you need some work on both the units and the formulas. If you check your formulas, you will see that the units don't work out.

Answer 3

sorry. I figured the distance in meters, not the velocity in m/s. See whether you can fix my mistake.