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/sec^{2}

2. Radial acceleration is a_{r} = r^{2},
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/sec^{2}

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/sec^{2}

5. Again tangential acceleration is always constant
a_{t} = 0.35m/sec^{2}

6. Radial acceleration -

= (2×0.7×2?/3)^{0.5}

a_{r} = 0.5×(2×0.7×2?/3) = 1.466 m/sec^{2}

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