A 60cm diameter bike wheel starts at rest and develops an angular speed of 12.0 rad/s in 10 seconds. What linear distance does the bike travel?
Average speed* time
= (1/2)*(final speed)*time
= (1/2)*R*w*time
= (1/2)*(0.60 m)*12 rad/s*10 s
= 36 m
a clothes washer starts from rest and spins up with an angular accceleration of 10/rad/s^2. Determine the angle through which the washer has moved afer 6 seconds.
To find the linear distance the bike travels, we need to use the relationship between linear distance, angular speed, and radius.
The formula is:
Linear distance = Angular speed x Radius
First, let's convert the diameter of the bike wheel into its radius. We know that the diameter is given as 60 cm, so the radius is half of that.
Radius = Diameter / 2 = 60 cm / 2 = 30 cm
Now, let's convert the radius from centimeters to meters since the angular speed is given in radians per second, which is the SI unit.
Radius = 30 cm = 30 cm x (1 m / 100 cm) = 0.3 m
Now, we can use the formula to find the linear distance traveled:
Linear distance = Angular speed x Radius
Linear distance = 12.0 rad/s x 0.3 m = 3.6 m
Therefore, the linear distance the bike travels is 3.6 meters.