Final answer:
To calculate the linear speed of a point on an 8-inch disk, measure the time for 10 revolutions, determine the angular velocity, and use the formula V = Rω, with the disk's radius in inches, to find the speed in inches per second.
Step-by-step explanation:
To find the linear speed of a point on the circumference of an 8-inch disk, we first need to determine its angular velocity. Once we have the angular velocity, we can use the formula V = Rω to calculate the linear speed, where V is the linear speed, R is the radius of the disk, and ω (omega) is the angular velocity. The radius R will be half of the disk diameter, which is 4 inches.
Assuming we measured the time it took for the disk to complete 10 revolutions and found this to be 't' seconds, we would calculate the angular velocity as ω = (10 revolutions / t seconds) × (2π radians/revolution). This would give us the angular velocity in radians per second.
To complete the calculation, we would then multiply the radius of the disk by the angular velocity to find the linear speed: V = Rω = 4 inches × (20π / t) rad/s. The answer will be in inches per second, and it should be rounded to the nearest hundredth as required.