4. A horse on a merry go round is 7 m from the center and travels at 10km/hr. What is its angular speed?
arc = rθ
in our case: arc = 7θ
d(arc)/dt = 7 dθ/dt
10000 m/hr = 7 m dθ/dt
dθ/dt = 10000/7 rad/hr or appr 1428.57 rad/hr = appr 23.8 rad/min
or , non-Calculus way
circumference = 14π = 43.98 m
speed = 10 km/h = 10000/60 m/min = 166.667 m/min
time to complete one revolution = distance/rate = 43.98/166.667 = appr .264 min
angular velocity = 2π rad/.264 min = 23.81 rad/min , same as above
You didn't say what units of time was required.
V = 10km/h = 10,000m/3600s = 2.78 m/s.
Cir. = pi * 2r = 3.14 * 14 = 44.0 m.
Va = 2.78m/s * 6.28rad/44m = 0.40 rad/s.
Well, let's calculate it, shall we? So, first, we have the distance from the center, which is 7 meters. And the horse is traveling at a speed of 10 km/hr. Now, we need to convert that speed to meters per second because we're dealing with meters here, not kilometers. So, let's see, 10 km/hr... okay, let's carry the one, divide by pi, multiply by the number of apples in the fruit basket, subtract the circumference of the Earth... and - voila! - the horse's angular speed is... uh oh, I seem to have misplaced my calculations. Sorry about that! But hey, what's the hurry? The horse is just going around in circles anyway, so let's just enjoy the ride and leave the math to the mathematicians, shall we? Wheee!
To find the angular speed of a horse on a merry-go-round, we need to know the linear speed of the horse and the radius of the circle.
Given:
- Linear speed of the horse: 10 km/hr
- Radius of the circle: 7 m
We need to convert the linear speed from km/hr to m/s, as the radius is given in meters.
1 km = 1000 m
1 hr = 3600 s
Converting 10 km/hr to m/s:
(10 km/hr) x (1000 m/1 km) x (1 hr/3600 s) = 10000/3600 m/s = 2.78 m/s (rounded to 2 decimal places)
Now, we can calculate the angular speed using the formula:
Angular speed (ω) = Linear speed (v) / Radius (r)
Angular speed (ω) = 2.78 m/s / 7 m = 0.3971 rad/s (rounded to 4 decimal places)
Therefore, the angular speed of the horse on the merry-go-round is approximately 0.3971 rad/s.
To find the angular speed of the horse on the merry-go-round, we need to use the formula:
Angular Speed (ω) = Linear Speed (v) / Radius (r)
Given that the linear speed is 10 km/hr and the radius is 7 m, we must convert the linear speed from km/hr to m/s since the radius is in meters.
1 km = 1000 m
1 hr = 3600 s
Converting 10 km/hr to m/s:
10 km/hr * (1000 m / 1 km) * (1 hr / 3600 s) = 10 * 1000 / 3600 = 2.78 m/s
Now, substituting the values into the formula:
Angular Speed (ω) = Linear Speed (v) / Radius (r)
ω = 2.78 m/s / 7 m = 0.3971 rad/s
Therefore, the angular speed of the horse on the merry-go-round is approximately 0.3971 rad/s.