Answer to Question #80507 in Mechanics | Relativity for Ankit

Question

A wheel 2.0 m in diameter lies in the vertical plane and rotates about its central axis
with a constant angular acceleration of 4.0 rad s−2. The wheel starts at rest at t = 0 and
the radius vector of a point A on the wheel makes an angle of 60º with the horizontal at
this instant. Calculate the angular speed of the wheel, the angular position of the point A
and the total acceleration at t = 2.0s.

Answer 1

Angular speed of the wheel at t = 2.0s
ω=ω_0+ξ·t=0+4·2=8 rad/sec
Angular position of the point A at t = 2.0s
=_0+(ξ·t^2)/2=π/3+(4·2^2)/2=π/3+2.55·π=2.88·π
Angular position of the point A at t = 2.0s is 2.88·π=158.4 ̊
Acceleration at t = 2.0s
a_τ=ξ·R=4·2=8 m/〖sec〗^2
a_n=ω^2·R=8^2·2=128 m/〖sec〗^2