Question

A flywheel with a radius of 0.500 m starts from rest and accelerates with a constant angular acceleration of 0.700 rad/s2 .

1.Compute the magnitude of the tangential acceleration of a point on its rim at the start.

2.Compute the magnitude of the radial acceleration of a point on its rim at the start.

3.Compute the magnitude of the tangential acceleration of a point on its rim after it has turned through 60.0 ?.

4.Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 60.0 ?.

5.Compute the magnitude of the tangential acceleration of a point on its rim after it has turned through 120.0 ?.

6.Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 120.0 ?.

Answer 1

1. Tangential acceleration is given by a_t = r = 0.5×0.7 = 0.35m/sec²

2. Radial acceleration is a_r = r², here initial = 0

So initial radial acceleration = 0

3 tangential acceleration is constant as it does not depend on angular velocity so a_t = 0.35m/sec²

4. After 60 degree angular displacement

= (2)^0.5 = (2×0.7×?/3)^0.5 = 1.211 rad/sec

a_r = 0.5×(1.211)² = 0.7331 m/sec²

5. Again tangential acceleration is always constant a_t = 0.35m/sec²

6. Radial acceleration -

= (2×0.7×2?/3)^0.5

a_r = 0.5×(2×0.7×2?/3) = 1.466 m/sec²