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
i. incorrect.
The angle turned in radians?
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)
(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.
sorry. I figured the distance in meters, not the velocity in m/s. See whether you can fix my mistake.
To calculate the angle turned in radians, you can use the formula θ = degree * 2π/360. In this case, the number of revolutions is given as 200. Convert that to degrees by multiplying 200 by 360 (since one revolution is equal to 360 degrees). Then, divide the result by 360 to obtain the number of degrees. Finally, multiply the number of degrees by 2π/360 to convert to radians.
So, θ = 200 * 2π/360 = 3.49 radians.
To calculate the angular velocity in radians per second, you need to divide the angle (in radians) by the time taken for that rotation. As given, the time taken is 24 seconds.
So, ω = θ / t = 3.49 / 24 = 0.145 radians per second.
If the diameter of the wheel is 0.5 meters, the radius would be half of that, which is 0.25 meters.
To calculate the linear velocity of the car, you can use the formula v = ω * r, where ω is the angular velocity and r is the radius of the wheel.
So, v = 0.145 * 0.25 = 0.0725 meters per second.