A car's wheel of radius r=50cm goes through 5000rev in 1min. find the car's average angular velocity,and how far it travels along the ground in 1min. The linear speed v and angular speed w of the point of a rotating body are connected by the equation v=wr. where r is the distance of the point from the axis of rotation
Please answer
To find the car's average angular velocity, we need to divide the total angle covered by the wheel in one minute by the time it took to complete those revolutions.
1. First, we need to find the total angle covered by the wheel. We know that the wheel went through 5000 revolutions in 1 minute, and since each revolution corresponds to a full circle of 360 degrees or 2π radians, the total angle covered is 5000 revolutions * 2π radians/revolution.
Total angle = 5000 * 2π = 10000π radians
2. Next, we need to divide the total angle covered by the time it took to complete those revolutions (1 minute) to find the average angular velocity.
Average angular velocity = Total angle / Time
Average angular velocity = 10000π radians / 1 minute
Now, to find how far the car travels along the ground in 1 minute, we need to use the equation v = w * r, where v is the linear speed, w is the angular speed, and r is the distance of the point from the axis of rotation (which is the wheel's radius in this case).
3. The linear speed v is the distance traveled per unit of time, which is the speed of the car. We can find it by using the equation v = w * r, where w is the average angular velocity we found earlier and r is the radius of the wheel.
Linear speed v = Average angular velocity * radius
Linear speed v = 10000π radians/minute * 50 cm
To convert the units to a more convenient form, we need to change radians/minute to cm/minute. Since the radius is given in centimeters, the conversion factor from radians to centimeters is the circumference of a circle (2πr).
Circumference = 2π * 50 cm = 100π cm
4. Finally, we calculate the linear speed and multiply it by the time (1 minute) to find the distance traveled.
Linear speed v = 10000π * 50 cm / minute
Distance traveled = Linear speed * Time
Distance traveled = (10000π * 50 cm / minute) * 1 minute
By evaluating the expressions, you will find the car's average angular velocity and how far it travels along the ground in 1 minute.