A group of students observes that a wooden block (m = 0.40 kg) on the end of a string with a radius of 0.7 meters makes 9 rotations in 20.7 seconds when twirled.
What is the block's tangential (linear) speed?
What is the block's angular speed?
tan speed = 2 * π * 0.7 m * 9 / 20.7 = t m/s
ang speed = 2 * π * 9 / 20.7 = a rad/s
To calculate the tangential (linear) speed of the block, we can use the formula:
Tangential speed = (2π * radius) / time
Here are the steps to find the tangential speed:
1. Calculate the circumference of the circular path using the radius:
Circumference = 2π * radius
2. Divide the circumference by the time taken for the rotations:
Tangential speed = Circumference / time
To find the angular speed of the block, we can use the formula:
Angular speed = (2π * number of rotations) / time
Here are the steps to find the angular speed:
1. Multiply the number of rotations by 2π (since one rotation is equal to 2π radians):
Angular speed = (2π * number of rotations) / time
Now, let's calculate the values:
Given:
Mass of the wooden block (m) = 0.40 kg
Radius (r) = 0.7 meters
Number of rotations = 9
Time (t) = 20.7 seconds
Tangential speed:
Circumference = 2π * radius = 2π * 0.7 meters
Tangential speed = Circumference / time
Angular speed:
Angular speed = (2π * number of rotations) / time
Plug in the values and perform the calculations to find the answers.