In dealing with nonuniform circular motion, as shown in Fig. 3.23, we should write Equation 3.16 as a r = v 2 / r , to show that this is only the radial component of the acceleration. Recognizing that v is the object’s speed, which changes only in the presence of tangential acceleration, differentiate this equation with respect to time to find a relation between the magnitude of the tangential acceleration and the rate of change of the magnitude of the radial acceleration. Assume the radius stays constant.
In dealing with nonuniform circular motion, as shown in Fig. 3.23, we should write Equation 3.16 as a r = v 2 / r , to show that this is only the radial component of the acceleration. Recognizing that v is the object’s speed, which changes only in the presence of tangential acceleration, differentiate this equation with respect to time to find a relation between the magnitude of the tangential acceleration and the rate of change of the magnitude of the radial acceleration. Assume the radius stays constant.
In dealing with nonuniform circular motion, as shown in Fig. 3.23, we should write Equation 3.16 as ar = v2/r, to show that this is only the radial component of the acceleration. Recognizing that v is the object’s speed, which changes only in the presence of tangential acceleration, differentiate this equation with respect to time to find a relation between the magnitude of the tangential acceleration and the rate of change of the magnitude of the radial acceleration. Assume the radius stays constant.
A particle moves through 3-space in such a way that its acceleration is
a(t)= 8sin 2ri +8cos 2tj+e'k .
where t is time measured in seconds. The initial velocity of the particle is v, =
2i – 3j+k.
At time t = t , find
i)
the velocity vector of the particle.
ii)
the scalar tangential and normal components of acceleration.
The radius of the earth is R. At what distance above the earth's surface, in terms of R , is the acceleration due to gravity = 2.5 m/s2 ?
At approximately
(answer) × R above the earth’s surface.
A rotating fan completes 1200 revolutions every minute. Consider the tip of a blade, at a radius of 0.15 m. (a) Through what distance does the tip move in one revolution? What are (b) the tip’s speed and (c) the magnitude of its acceleration? (d) What is the period of the motion?
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