Q#1
Can an object be in pure translation as well as in pure rotation?
Answer:
No. In pure translation, each particle of the body moves in parallel lines while in a pure rotation the particles of a body move in concentric circles, Both cannot be true at the same time.
Q#2
A simple pendulum is a point mass suspended by a light thread from a fixed point. The particle is displaced towards one side and then released. It makes small oscillations. Is the motion of such a simple pendulum a pure rotation? If yes where is the axis of rotation?
Answer:
Since in a pure rotation all particles of a body move in concentric circles, hence this motion of a simple pendulum is a pure rotation, only the direction of motion reverses periodically. The axis of rotation is the line perpendicular to the plane of rotation and passing through the fixed point where the thread of the pendulum is tied.
Since the oscillations are small, for all practical purposes the movement of the ball can be assumed on a straight line and also the motion can be taken as periodic and Simple Harmonic motion can be assumed.
But these are the differences in theory and practice.
Q#3
In a rotating body, a = αr, v = ωr. Thus a/α = v/ω. Can you use the theorems of ratio and proportion studied in algebra so as to write
(a + α)/(a - α) = (v + ω)/(v - ω)?
In the given relations there are five unknowns. When the first one is divided by the second, in fact, one unknown "r" is being eliminated. But if we use the theorems of ratio and proportion to write it as
(a + α)/(a - α) = (v + ω)/(v - ω)
we are not eliminating any unknown but complicating the relation a/α = v/ω.
Also, this equation is not dimensionally correct. So, we can not write it like that.
Q#4
A ball is whirled in a circle by attaching it to a fixed point with a string. Is there an angular rotation of the ball about its center? If yes, is this angular velocity equal to the angular velocity of the ball about the fixed point?
Answer:
Yes the ball has an angular rotation about its center. If we notice the position of the point on the ball where it is tied with the string, we can see that it is moving about its center as its position changes. This point again comes to the same position when the ball makes a complete revolution around the fixed point. Thus, the ball rotates about its center through 360° in the same time in which the ball revolves through 360° around the fixed point. Hence the angular velocity of the ball about its center is equal to the angular velocity of the ball about the fixed point.
Q#5
The moon rotates about the earth in such a way that only one hemisphere of the moon faces the earth (figure-10Q1). Can we ever see the "other" face of the moon from the earth? Can a person on the moon ever see all the faces of the earth?
Answer:
Since only one hemisphere of the moon faces the earth, we can never see the "other" face of the moon from the earth.
But a person on the moon can see all the faces of the earth. The reason is that the time period and the direction of rotation of the moon is exactly the same as the revolution around the earth (about 28 days)-just like a ball being rotated in a circle around a fixed point. But the time period of the earth's rotation is not the same which is about 24 hours. So during one revolution of the moon, the earth rotates about 28 times. So a person on the facing side of the moon can see all faces of the earth.
The torque of the weight of a body about any vertical axis is zero. Is it always correct?
Answer:
A force can only produce a torque around an axis if it has a component in the plane perpendicular to the axis and this component does not pass through the point of intersection of this plane and the axis. In the given case, the force of weight is parallel to any given vertical axis, hence it can not have a component in a plane perpendicular to this axis (Horizontal Plane). So it can not produce a torque about any vertical axis i.e. torque is zero. It is always correct.
Q#7
The torque of a force Fabout a point is defined as Γ = r x F. Suppose r, F and Γ are all nonzero. Is r x Γ ||F always true? Is it ever true?
Answer:
The direction of the vector Γ (torque) is perpendicular to the plane in which r and F lie. The direction of the vector r x Γ will be perpendicular to the plane in which r and Γ lie. So, it is not always true that r x Γ||F. It can only be true if r丄F but their directions will be opposite.
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