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 marble slides down on a curved path defined by the parabola y = 0.4x2. When it is at point “A” (xA = 2m; yA = 1.6m), the velocity of the marble v = 8m/s and the tangental acceleration due to gravity is
dv / dt = 4ms2. Calculate the normal component and the total magnitude of the accelarion of the mable in that instant.
A particle travels around a circular path having a radius of 50 m. If it is initiallytraveling with a speed of 10 m/s and its speed then increases at a rate of a (v) = (0.05v) m/s 2 , thendetermine the magnitude of the particle’s acceleration four seconds later.
A skater is gliding along the ice at 2.2 m/s, when she undergoes an acceleration of magnitude 1.2 m/s2 for 3.0 s. At the end of that time she is moving at 5.8 m/s.
(a) What must be the angle between the acceleration vector and the initial velocity vector?
Chapter 3 Solutions
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