a skater holds her arms outstretched as she spins at 140 rpm. What is the speed of her hands if they are 125 cm apart?

speed=wr=140r/m*2PIrad/rev*1min/60sec*1.25/2m

assuming the hands are equally spaced from the cneter of rotation

Well, if a skater's arms are outstretched while spinning, it's safe to say she's trying to give the world a big "air hug"! Now, let's calculate the speed of her hands as she spins.

First, we need to convert the rotation rate from rpm (revolutions per minute) to revolutions per second. Since there are 60 seconds in a minute, the skater spins at a rate of 140/60 = 2.33 revolutions per second.

Now, let's find out the distance her hands travel in one revolution. Since her hands are 125 cm apart, when the skater completes one full rotation, her hands form a circular path with a circumference of 2π × r, where r is the distance between her hands.

Substituting the values, the distance traveled in one revolution is approximately 2π × 125 cm ≈ 785.4 cm.

Finally, to calculate the speed of her hands, we multiply the distance traveled in one revolution by the number of revolutions per second:
Speed = 785.4 cm/rev × 2.33 rev/s ≈ 1831.5 cm/s.

So, it seems like her hands are moving at a speed of around 1831.5 cm/s - quite fast! I hope she's able to grab any "air high fives" that come her way!

To find the speed of the skater's hands, you need to calculate the linear velocity. The linear velocity is the distance traveled per unit of time.

First, let's convert the given speed from revolutions per minute (rpm) to revolutions per second (rps). There are 60 seconds in a minute, so we have:

Speed (rps) = 140 rpm / 60 = 2.33 rps

Next, we need to find the circumference of the circle that the hands trace. The circumference of a circle is given by the formula:

Circumference = 2 * π * radius

Since the hands are 125 cm apart, the radius of the circle is half of this distance:

Radius = 125 cm / 2 = 62.5 cm

Now we can calculate the circumference:

Circumference = 2 * π * 62.5 cm

Using the value of π as approximately 3.14, we get:

Circumference ≈ 2 * 3.14 * 62.5 cm ≈ 392.5 cm

Finally, we can calculate the linear velocity using the formula:

Linear Velocity = Circumference * Speed

Linear Velocity = 392.5 cm * 2.33 rps

Calculating this value, we get:

Linear Velocity ≈ 914.725 cm/s

Therefore, the speed of the skater's hands is approximately 914.725 cm/s.

To find the speed of the skater's hands, we need to calculate the circumference covered by her hands in one revolution.

The circumference of a circle can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius of the circle.

In this case, the radius is half the distance between her hands, which is 125 cm. So the radius, r, would be 62.5 cm.

Next, we need to calculate the circumference covered by her hands in one revolution. Since she spins at 140 rpm (revolutions per minute), we need to convert this to revolutions per second. To do this, divide 140 by 60 (since there are 60 seconds in a minute):

140 rpm / 60 = 2.33 revolutions per second.

Now that we know the number of revolutions per second, we can calculate the speed by multiplying the circumference by the number of revolutions:

Speed = Circumference x Revolutions per second

Speed = (2π x 62.5 cm) x 2.33 revolutions per second

Speed ≈ 385.94 cm/s

Therefore, the speed of her hands is approximately 385.94 cm/s.