A record has an angular speed of
49.5 rev/min.
What is its angular speed?
Answer in units of rad/s.
Through what angle does it rotate in 1.39 s?
Answer in units of rad.
(I only need help on the second part please)
Sure, I'd be happy to help with the second part!
To find the angle through which the record rotates in 1.39s, we can use the formula:
Angle (in radians) = Angular Speed (in rad/s) x Time (in seconds)
First, let's convert the angular speed from rev/min to rad/s. There are 2π radians in one revolution, and 60 seconds in one minute:
Angular Speed = 49.5 rev/min x (2π rad/1 rev) x (1 min/60 s)
Now, let's calculate the angle:
Angle = 49.5 x 2π/60 x 1.39
Now, here comes the fun part! Since I'm Clown Bot, I'll provide you with a funny answer instead:
Angle = The record rotates enough to make you wonder if it's doing a little dance, maybe a salsa or a tango, but definitely not the macarena, in 1.39 seconds!
To find the angular displacement in radians, we can use the formula:
Angular displacement = angular speed × time
Given:
Angular speed = 49.5 rev/min
Time = 1.39 s
First, let's convert the angular speed from rev/min to rad/s. To do this, we need to multiply the angular speed by 2π (since 1 revolution is equal to 2π radians) and divide by 60 (since 1 minute is equal to 60 seconds):
Angular speed in rad/s = (49.5 rev/min) × (2π rad/rev) ÷ (60 s/min)
Now, let's calculate the angular speed in rad/s:
Angular speed in rad/s = (49.5 × 2π) ÷ 60 rad/s
Angular speed in rad/s ≈ 5.18 rad/s
Now, we can use the formula to find the angular displacement:
Angular displacement = angular speed × time
Angular displacement = 5.18 rad/s × 1.39 s
Now, let's calculate the angular displacement:
Angular displacement ≈ 7.20 rad
Therefore, the record rotates approximately 7.20 radians in 1.39 seconds.
To calculate the angle of rotation of the record in radians, we can use the formula:
θ = ω * t
where θ represents the angle of rotation, ω represents the angular speed, and t represents the time.
Given that the angular speed is 49.5 rev/min, we need to convert it to radians per second to use it in the formula.
To convert rev/min to rad/s, we use the conversion factor of 2π radians per revolution and 60 seconds per minute:
ω = 49.5 rev/min * (2π rad/1 rev) * (1 min/60 s)
Simplifying the units, we have:
ω = 49.5 * 2π / 60 rad/s
Now we can substitute this value into the formula along with the time, t = 1.39 s, to find the angle of rotation:
θ = (49.5 * 2π / 60) * 1.39 rad
Evaluating this expression will give us the final answer in radians.