A grinding wheel with a 28cm diameter spins at rate of 2020 revolutions per minute. What is the linear speed of thge rim of the wheel?
One diameter covers 28π cm
So in 1 minute the rim covers 2020(28π) cm
so the linear speed of the rim = 56560π cm/min
To find the linear speed of the rim of a grinding wheel, we first need to calculate the circumference of the wheel.
The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. In this case, the diameter of the grinding wheel is given as 28 cm.
C = π × 28 cm
C ≈ 87.9646 cm (approximately)
Now that we know the circumference of the wheel, we can calculate the linear speed. The linear speed is the distance traveled per unit of time.
The formula for linear speed is v = distance/time, where v is the linear speed, distance is the distance traveled, and time is the time taken.
Since the wheel completes 2020 revolutions per minute, we can calculate the distance traveled per minute by multiplying the circumference of the wheel with the number of revolutions:
Distance per minute = C × number of revolutions
Distance per minute = 87.9646 cm × 2020 revolutions
Distance per minute ≈ 177,413.792 cm (approximately)
To convert the distance per minute to the linear speed per minute, we just divide by the time taken:
Linear speed per minute = Distance per minute / time taken
Linear speed per minute = 177,413.792 cm / 1 minute
Linear speed per minute ≈ 177,413.792 cm/min (approximately)
Therefore, the linear speed of the rim of the grinding wheel is approximately 177,413.792 cm/min.