An automobile moves on a circular track of radius 1.02 km. It starts from rest from the point (x, y ) = (1.02 km, 0 km) and moves counterclockwise with a steady tangential acceleration such that it returns to the starting point with a speed of 29.3 m/s after one lap. (The origin of the Cartesian coordinate system is at the center of the circular track.) What are the car's position and velocity vectors when it is one-eighth of the way around the track? Express the vectors in terms of the unit vectors along the x- and y-axes. r = ( _____ i + _____ j) km v = ( _____ i + _____ j) m/s
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
An automobile moves on a circular track of radius 1.02 km. It starts from rest from the point (x, y ) = (1.02 km, 0 km) and moves counterclockwise with a steady tangential acceleration such that it returns to the starting point with a speed of 29.3 m/s after one lap. (The origin of the Cartesian coordinate system is at the center of the circular track.)
What are the car's position and velocity vectors when it is one-eighth of the way around the track? Express the vectors in terms of the unit vectors along the x- and y-axes.
r = ( _____ i + _____ j) km
v = ( _____ i + _____ j) m/s
What is the tangential acceleration at this point?
_______ m/s2
What is the centripetal acceleration at this point?
_______ m/s2
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