Question

a truck is moving at a rate of 90km/hr, and the diameter of its wheel is 1 meter. find the angular speed of the wheels in radians per second.

Answer 1

Ok. The circumference of a circle is 2.pi.r where r is the radius. The wheel has a radius of r = 1/2 meters, hence with one rotation of the wheel, the truck will travel a distance of
2.pi.(1/2 meters) = pi meters.

So far so good?

Now what we want to figure out is how many rotations the wheel makes per second; call that number R. (Not little r from above.)

Once we know that, the angular velocity will be 2.pi.R, because every rotation is equivalent to 2.pi radians.

So what you need to do now is calculate R. Use the result above and figure out how fast
90 km/hr is in m/s.

90 km/hr = 90,000 m/hr
= 90,000/60 m/min
= 1,500 m/min
= 1,500/60 m/sec
= 25 m/sec

Hence the truck is traveling at a speed of 25 m/sec.

Now, given that how many rotations, R, does the wheel make?

We know it travels a distance of pi with one rotation. Hence per second the number of rotations is

R = 25/pi 1/sec

Hence the angular velocity = (2.pi radians)(25/pi 1/sec)
= 50 radians/sec

Answer 2

could you help me with another one?