Help please? Having trouble with this.
A race car makes two and half laps around a circular track in 3.0 min. What is the car's average angular speed?
To find the car's average angular speed, we need to know the total angle covered by the car and the time taken.
Step 1: Find the total angle covered by the car.
The car completes two and a half laps around the circular track. Since one lap is equivalent to a full circle, the angle covered by the car is 2.5 times the angle of a full circle, which is 2.5 x 360 degrees.
Total angle covered = 2.5 x 360 = 900 degrees.
Step 2: Convert the time to seconds.
The given time is 3.0 minutes. To calculate the average angular speed, we need the time in seconds since angular speed is measured in units of radians per second.
Time in seconds = 3.0 minutes x 60 = 180 seconds.
Step 3: Calculate the average angular speed.
Angular speed (ω) is given by the formula:
ω = (Total angle covered) / (Time taken)
Substituting the values we found earlier:
ω = 900 degrees / 180 seconds.
However, we need to convert the angle to radians since the angular speed is usually measured in radians.
1 degree = π/180 radians.
ω = (900 x π/180) radians / 180 seconds.
Step 4: Simplify the expression.
ω = (5π/2) radians / 180 seconds.
Therefore, the car's average angular speed is (5π/2) radians per 180 seconds.
To find the car's average angular speed, we need to calculate the number of radians the car rotates through in a given time. The formula for angular speed (ω) is:
ω = θ/t
Where:
ω - angular speed
θ - angle rotated
t - time interval
In this case, the car makes two and a half laps around the circular track. Since one lap is equal to 2π radians, two and a half laps would be:
2.5 * 2π = 5π radians
The time taken by the car is 3.0 minutes. We need to convert this into seconds, as angular speed is typically measured in radians per second:
3.0 minutes * 60 seconds/minute = 180 seconds
Now we can use the formula to find the angular speed:
ω = θ/t
ω = (5π radians) / (180 seconds)
Calculating this expression will give us the car's average angular speed.
one lap (circle) is 2π radians
5/2 * 2π radians in 3.0 min (180 sec)
angular speed is rad/s or rad/min