A wheel of a child's car revolves at 15 rpm.
a) What is the angular velocity of the wheel in radians per seconds?
b) A painted dot on the circumference of the wheel is 12 cm from the center of rotation of the wheel. How far does the dot travel in 5s?
The radius of the wheel is 12 cm, therefore the circumference ( 2pi r) = 2 .3/14. 12 is equal to 75.39822369 . According to the previous section of the question, the wheel rotates 15 times per minute( 60 seconds); therefore 15 times 75.39822369 that is equal to 904.7786842 , is the the total distance the wheel revolves in 60 seconds. Through a simple equation , 94.2477961 cm is revolved in 5 seconds.
ω = 15 rev/min * 1min/60s * 2πrad/rev = ? rad/s
s = rθ = 12cm * ω rad/s * rs = ? cm
Given the radius of the tire is 1.2", what is the angular velocity of the wheels in RPM?
To find the angular velocity of the wheel in radians per second, we need to convert the given value of revolutions per minute (rpm) to radians per second.
a) To convert revolutions per minute (rpm) to radians per second, we can use the following conversion factor:
1 revolution = 2π radians
First, let's convert the given value of 15 rpm to revolutions per second:
15 rpm * (1/60) revs/sec = 0.25 revs/sec
Next, we can convert the revolutions per second to radians per second:
0.25 revs/sec * 2π radians/1 revolution = 0.25 * 2π radians/sec ≈ 1.57 radians/sec
Therefore, the angular velocity of the wheel is approximately 1.57 radians per second.
b) To find how far the dot on the circumference of the wheel travels in 5 seconds, we can use the formula:
Distance = (Radius of the wheel) * (Angle turned in radians)
First, let's convert the given distance of 12 cm to meters:
12 cm * (1 meter/100 cm) = 0.12 meters
Next, we need to find the angle turned by the dot in 5 seconds. The angular velocity is given in radians per second, so we can use the formula:
Angle = (Angular velocity) * (Time)
Angle = 1.57 radians/sec * 5 sec = 7.85 radians
Finally, we can calculate the distance traveled by the dot on the wheel's circumference:
Distance = 0.12 meters * 7.85 radians = 0.942 meters
Therefore, the dot on the wheel travels approximately 0.942 meters in 5 seconds.