A wheel starts from rest with constant angular acceleration of 3rad/s^2?

Question

(a) After 7 s, what is its angular velocity?
correct check mark rad/s
(b) Through what angle has the wheel turned?
rad
(c) How many revolutions has it made?
rev
(d) What is the speed of a point 0.7 m from the axis of rotation?
m/s
What is the magnitude of the total acceleration of the same point?
m/s2

Answer 1

Ok, let's remeber the formulas :

Wf = Wo +/- at

angle = Wo*t +/- 1/2*a*t^2

Wf^2 = Wo^2 +/- 2*a*angle

angle = angle in radians

a = angular acceleration

Wf = final angular velocity

Wo = initial angular velocity

(a) After 7 s, what is its angular velocity? a = 3 rad/s^2 wo = 0

wf = 0 + 3*7 = 21 rad / s >>> final angular velocity

(b) Through what angle has the wheel turned?
rad

angle = 0*t + 3*49 / 2 = 73.5 radians

(c) How many revolutions has it made?
rev

revolutions = how many times did the wheel complete 2pi radians.

pi = 3.1416..

73.5 / 2*pi = 11.7 rev