Final answer:
To calculate the linear velocity of a point on the circumference of a vinyl record with a 29 cm diameter and 90 rpm, convert the diameter to radius in meters, find the angular velocity in radians per second, and apply the formula v = r * ω. The resulting linear velocity is approximately 4.115 meters/second.
Step-by-step explanation:
To find the linear velocity of a point on the circumference of the vinyl record, we must first convert the diameter of the record to meters. Since the diameter is given as 29 cm, we can convert it to meters by dividing it by 100, resulting in 0.29 meters. Next, the radius of the record is half of the diameter, so the radius r is 0.29 meters / 2 = 0.145 meters.
Now, we know the record makes 90 rotations per minute (rpm). To find the linear velocity, we can use the formula v = r × ω, where ω (omega) is the angular velocity in radians per second. We need to convert the rotations per minute to radians per second. There are 2π radians in one rotation, and 60 seconds in one minute, so:
ω = 90 rpm × (2π radians/rotation) × (1 minute/60 seconds) = 9 π radians/second
Finally, we can calculate the linear velocity as follows:
v = 0.145 meters × 9 π radians/second ≈ 4.115 meters/second
Therefore, the linear velocity of a point on the circumference of the disk is approximately 4.115 meters/second.