Question

The rotation of a flywheel is governed by the equation w = 3t 2 - 2t + 2 where w
is in radians per second and t is in second. After 1 second from the start the
angular displacement was 4 radians. Then the equation for angular displacement
qis​

Answer 1

The scattering of light is the phenomenon by which a beam of light is redirected in different directions on interacting with the particles present in the medium. The sky appears blue because the fine particles in the atmosphere scatter blue light the most among all the components of white light.

Answer 2

Concept:

• Rotational motion
• An object moving around on a fixed orbital path in a circle is said to be rotating.
• There is no difference between linear or translational dynamics and the dynamics of circular motion.
• Angular velocity w
• Angular displacement θ
• Integration

Given:

• w = 3t^2 - 2t + 2
• t = 1 s
• Angular displacement θ = 4 rad

Find:

• The equation for angular displacement

Solution:

w = dθ/dt

θ is the integration of w wrt t

θ = 3t^3/3 - 2t^2/2 + 2t + c

C is a constant

θ = t^3 - t^2 + 2t + c

at t = 1, θ = 4

4 = 1-1 +2 + c

4 = 2 + c

2 = c

The equation is

θ = t^3 - t^2 + 2t + 2

The equation for angular displacement is θ = t^3 - t^2 + 2t + 2.

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