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 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?
At t = 1.0s, the acceleration of a particle in an anti-clockwise circular motion is a=4i-3ja. It moves at constant speed. At time t = 5.0s, theparticle’s acceleration is given by a=-3i=(-4)j.(a) Draw the circle traced out by the particle and the acceleration vectorstogether with their components. Clearly show their directions.
b)Find the angle between the acceleration vectors
c) Find the radius of the path taken by the particle if t2 – t1 is less than oneperiod
A particle describes an UCM(uniform circular motion) with period 0.500 s and circle centered at the origin of the x and y coordinate system.
Let î and ȷ be the unit vectors along the x and y directions, respectively.
At instant t=0 the particle's acceleration vector (in m/s2) is a =2.30î.
What is its acceleration vector (in m/s2) at time t=2.50 s?
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