Rotation and Linear motion.. There are two kinds of circular motion. Can you recognise them on the minute hand of this clock? Any body will at once say the hour hand does a complete round in one hour. This is rotation or spinning. What is the other type of motion? Consider the blue and red paper markers on the minute hand. They also move with the hand. Do they have the same speed? The blue dot covers a larger circle than the red dot during the same time. So the blue dot has to be faster. This is the other type of motion, which is similar to linear motion. This is sometimes referred to as the orbital motion. Translational Motion considered for a quarter turn which was in 15 minutes. (900 s)
Rotation, can be measured by considering the turning angle.This is angular measurement. When the angle is considered, there is no difference between the red and blue points. Angular motion. When the minute hand does a round it has to cover 360° As we know the time it takes, the velocity can be determined. Let us take an example where the hand moved for 15 minutes.
Angular acceleration. Angular acceleration ,α = change in velocity ÷ time. α = ω f - ω i ÷ t. rad.s-2 Example. Muralitharan spins a cricket ball making an angular displacement of 4 rad. in 0.08 seconds. The radius of the bowler’s wrist is 3 cm. Assume that the starting angular velocity is zero and the acceleration was uniform. Find the following.
c) the maximum angular velocity. d) Angular acceleration. e) Spinning rate of the ball leaving the hand.
e) Final angular velocity = 100 rsd S-1. One turn = 2π radians. Turninings = 100 / 6.28 …….= 16 turns per second. Example 2 The graph shows the angular acceleration of a rotating disc against time. Find the following.
Rotational Inertia In translational motion, mass is the property that inhibits acceleration. Greater the mass slower the acceleration when a force is used. Acceleration is inversely proportional to mass. F = ma. In rotation the factor that inhibits acceleration, when a torque is used is INERTIA. (I) A torque is a force used to rotate and object. = F x lever arm. Considering inertia = I α, A and B are two wooden wheels that can rotate in a vertical plane. They are identical except for the way nails are embedded. In A the metal nails are closer to the axis while in B. they are closer to the circumference. Same torque is used on both. The figure shows that A had a higher acceleration than B. The difference is due to the difference in inertia of the two wheels. The Inertia of a body depends on how the mass is distributed. If there is more mass closer to the centre of rotation, the inertia will be lower than when the mass accumulates near the periphery. The inertia of some regular bodies can be found using these formulae. The unit for inertia is kg. m^{2 } (This is also called "Moment of Inertia"^{.}) ^{} |
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