The tires on a car have radius 14 inches. Find the angular speed of the car tire in
revolutions per second when it is traveling 70 mph. Find the angular speed at 80 mph.
The tires on a car are 15 inches. Find the linear speed of the car when the tires
are rotating at 900 revolutions per minute.
circumference of tire = 2π(14) = 28π inches
80 miles/hour
= 80(5280) ft / 60 minutes
= 7040 ft/min
= 7040(12) inches / 60 sec
= 1408 inches/sec
so the wheel is rotating 1408/(28π) times per second
= 16.001 times per sec or 960.4 rotations/min
the angular velocity is 960.4 rpm
You did not specify what units you wanted, I gave you two of them.
See if you can make the calculation changes to solve the second question.
To find the angular speed of a car tire, we can use the formula:
Angular speed (ω) = Linear speed (v) / Radius (r)
First, let's convert the speed from miles per hour to inches per second.
1 mile = 5280 feet
1 hour = 60 minutes
1 minute = 60 seconds
Therefore, 70 mph = (70 * 5280 * 12) / (60 * 60) inches/second = 92,800 inches/second.
Now, let's find the angular speed at 70 mph:
Angular speed (ω) = Linear speed (92,800 inches/second) / Radius (14 inches)
= 6640 revolutions/second
So, the angular speed of the car tire when it is traveling 70 mph is 6640 revolutions/second.
Similarly, for 80 mph:
80 mph = (80 * 5280 * 12) / (60 * 60) inches/second = 105,600 inches/second.
Angular speed (ω) = Linear speed (105,600 inches/second) / Radius (14 inches)
= 7,560 revolutions/second
So, the angular speed of the car tire when it is traveling 80 mph is 7,560 revolutions/second.
Now, let's find the linear speed of the car when the tires are rotating at 900 revolutions per minute.
Angular speed (ω) = 900 revolutions/minute
To find linear speed, we need to convert revolutions to inches and minutes to seconds.
1 revolution = 2πr inches
1 minute = 60 seconds
Linear speed (v) = Angular speed (900 revolutions/minute) * 2π * radius (15 inches) / 60
= 942.48 inches/second
So, the linear speed of the car when the tires are rotating at 900 revolutions per minute is 942.48 inches/second.
To find the angular speed of a car tire in revolutions per second, we can use the following formula:
Angular speed (in radians per second) = Linear speed / Tire radius
To convert the linear speed from mph to inches per second, we need to multiply by the conversion factor 5280 feet/mile * 12 inches/foot * 1 hour/3600 seconds.
So, for the first part of the question:
1. Convert 70 mph to inches per second:
Linear speed = 70 mph * 5280 ft/mile * 12 inches/ft * 1 hour/3600 seconds
Linear speed = 102.66 inches per second
2. Calculate the angular speed:
Angular speed = Linear speed / Tire radius
Angular speed = 102.66 inches per second / 14 inches
Angular speed ≈ 7.33 radians per second
So, the angular speed of the car tire when it is traveling at 70 mph is approximately 7.33 radians per second.
For the second part of the question:
1. Convert 80 mph to inches per second:
Linear speed = 80 mph * 5280 ft/mile * 12 inches/ft * 1 hour/3600 seconds
Linear speed = 117.33 inches per second
2. Calculate the angular speed:
Angular speed = Linear speed / Tire radius
Angular speed = 117.33 inches per second / 14 inches
Angular speed ≈ 8.38 radians per second
So, the angular speed of the car tire when it is traveling at 80 mph is approximately 8.38 radians per second.
Now, let's move on to the second question:
To find the linear speed of the car when the tires are rotating at 900 revolutions per minute, we can use the formula:
Linear speed = Angular speed * Tire radius
1. Convert 900 revolutions per minute to revolutions per second:
Angular speed = 900 revolutions per minute / 60 seconds
Angular speed = 15 radians per second
2. Calculate the linear speed:
Linear speed = Angular speed * Tire radius
Linear speed = 15 radians per second * 15 inches
Linear speed = 225 inches per second
So, the linear speed of the car when the tires are rotating at 900 revolutions per minute is 225 inches per second.