Final answer:
To find the speed of the skater's hands, convert 130 rpm to radians per second and multiply by the radius of 0.65 meters, which gives approximately 8.85 m/s as the linear speed of the skater's hands.
Step-by-step explanation:
To calculate the speed of a skater's hands as she spins, we need to convert the rotation from revolutions per minute (rpm) to radians per second, and then use the relationship between angular velocity and linear velocity.
First, note that 130 rpm is approximately 13.61 radians per second (since 130 rpm = 130 / 60 revolutions per second, and there are 2π radians in one revolution, the conversion is 130 / 60 * 2π = 13.61 radians per second). The skater's arms are 130 cm apart, meaning that her hands are 65 cm (or 0.65 m) from the axis of rotation. The linear speed is the product of the angular speed and the radius.
The speed of the skater's hands (v) can be found using the formula: v = ω * r, where ω is the angular velocity and r is the radius. Plugging in the values, we have v = 13.61 rad/s * 0.65 m, which gives us approximately 8.85 m/s. Therefore, the speed of the skater's hands is about 8.85 meters per second.