A wheel has a radius of 4.3 m How far path length does a point on the circumference travel if the wheel is rotated through angles of 30 30 rad and 30 rev respectively?

Answer 1

The diameter (i.e. the length of the outside) of the wheel is 4.3 meters times Pi (3.14) or abut 13.5 meters.

Circumference = 4.3 m x Pi = 4.3 x 3.14 = 13.5m

For a 30 degree rotation, the wagon will have moved forward a fraction of the wheel's circumference that is equal to the percentage of the wheel thatis represented by 30degrees. Since the circumference is represented by 360 dgrees, this percetange is 30/360.

Distance moved = (percentage of circumference represented by 30 degrees)x(circumference)

= (30 degrees/360 degrees)x(13.5m) = 1.125m or 1-1/8m

For a 30 rad rotation (rad=radians) , the wagon will have moved forward a multiple of the wheel's circumference that is equal to the multiple that is represented by 30radians. Since the there 2 times Pi radians per 360 degrees, there are 2xPi radians per circumference.

Thirty radians (in terms of circumference) = (number of radians)/radians per one circumference) =(30 radians)(1 circumference/2 x Pi radians) =15/Pi circumferences

Distance moved = (multiple of circumference represented by 30 radians)x(circumference)

= (15/Pi circumferences)x(4.3m x Pi) = 15x4.3 m = 64.5m

For 30 revolutions, the wagon will have moved forward 30 times the wheel's circumference because one revolution is equal to one circumference.

Thirty revolutions = number of revolutions x (number of circumferences/revolution) = 30 rev x (1 rev/1 circumference) = 30 circumferences

Distance moved = (30 circumferences)x(13.5m) = 405m

Answer 2

If the wheel is rotated through an angle of 30 radians, the path length traveled by a point on the circumference is given by the formula s = rθ, where r is the radius (4.3 m) and θ is the angle in radians (30). Therefore, the path length is s = 4.3 * 30 = 129 m. When rotated by 30 revolutions, the point on the circumference will complete one full revolution for each revolution of the wheel, so the path length traveled would be the circumference of the wheel, which is 2πr = 2π * 4.3 = 27.04 m.