Find the tangential and normal components of acceleration:

A fly wheel along diameter 400 mm begins from rest with constant angular acceleration 2 rad/sec². Find out the tangential & normal components of acceleration of a point on the rim, 3 seconds after the motion begins.

Solution

Radius of the wheel = 200 mm.

α = 2 rad / sec ² (constant )

ω = α t = 2 × 3 = 6 rad / sec

a = a_t  t^ + a_n n^

= a α_t t^  + a ω_n^²

= 200 × 2 t^ + 200 × 36 n^

= 400 t^ + 7200 n^

∴ a_t  = 400 mm / sec ²

a_n  = 7200 mm / sec²