A record has an angular speed of 47 rev/min. Through what angle does it rotate in 1.07 s? Answer in units of ra
To find the angle through which the record rotates in 1.07 seconds, we first need to convert the angular speed from revolutions per minute (rev/min) to radians per second (rad/s).
1 revolution = 2π radians
So, to convert from rev/min to rad/s, we can use the following conversion factor:
1 rev/min = (2π rad/1 rev) × (1 min/60 s) = π/30 rad/s
Now, we can calculate the angular speed in radians per second:
Angular speed = (47 rev/min) × (π/30 rad/s) ≈ 4.933 rad/s
Next, we can calculate the angle through which the record rotates in 1.07 seconds using the formula:
Angle = Angular speed × Time
Angle = (4.933 rad/s) × (1.07 s) ≈ 5.276 ra
Therefore, the record rotates through an angle of approximately 5.276 ra in 1.07 seconds.