a merry go round wheel rotates with an angular speed of 2 rad/s. consider two children on the wheel, one standing .5 m and the other 1.5 m away from the center of the wheel. the chid at 1.5 m distance is moving__________ times faster than the child at .5 m distance.
what is the tangential speed of the child at 1.5 m?
Tangential speed = rω
Since ω (angular speed) is constant, so the tangential speed is proportional to the radius.
To find the tangential speed, we can use the formula:
v = r * ω,
Where:
v is the tangential speed,
r is the distance from the center,
and ω (omega) is the angular speed.
In this case, we are given that the angular speed (ω) is 2 rad/s. We need to find the tangential speed (v) of the child at 1.5 m distance from the center.
To calculate the tangential speed, we can use the formula with the given values:
v = 1.5 m * 2 rad/s = 3 m/s.
Therefore, the tangential speed of the child at 1.5 m distance from the center is 3 m/s.
Now, let's find the ratio of the tangential speeds of the child at 1.5 m distance from the center to the child at 0.5 m distance from the center.
The child at 1.5 m distance has a tangential speed of 3 m/s, and the child at 0.5 m distance from the center has the same angular speed. The ratio of their tangential speeds will be:
Ratio = v1.5m / v0.5m,
Ratio = (1.5 m * 2 rad/s) / (0.5 m * 2 rad/s),
Ratio = 3 m/s / 1 m/s,
Ratio = 3.
Therefore, the child at 1.5 m distance is moving 3 times faster than the child at 0.5 m distance from the center.