A rotating wheel with diameter 0.800 m is speeding up with constant angular acceleration. The speed of a point on the rim of the wheel increases from 3.00 m/s to 6.00 m/s while the wheel turns through 4.00 revolutions. Required:
What is the angular acceleration of the wheel?

The angular acceleration of the wheel is 3.357rad/s²

Explanation:

Given;

Diameter of the wheel, d = 0.8 m

radius of the wheel, r = 0.4 m

initial velocity of the wheel, u = 3 m/s

final velocity of the wheel, v = 6 m/s

number of revolutions of the wheel, N = 4 rev.

Convert the linear velocity in m/s  to angular velocity in rad/s;

v = ωr

ω = v / r

initial angular velocity,

final angular velocity,

The angular acceleration of the wheel is calculated as;

where;

α is the angular acceleration (rad / s²)

θ is the angular rotation (rad)

θ = Number of revolutions x 2π rad/rev

  =  4 rev. x 2π rad/rev

  = 25.136 rad.

α = 3.357 rad/s²

Therefore, the angular acceleration of the wheel is 3.357rad/s²

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles