Final answer:
Uniform circular motion involves a body moving in a circle at constant speed with acceleration directed towards the center, known as centripetal acceleration. The angle between acceleration and velocity is always 90 degrees in such a motion. Calculations for forces and accelerations in circular motion involve the mass, velocity, and radius for centripetal force and change in angular velocity over time for angular acceleration.
Step-by-step explanation:
The student's question pertains to uniform circular motion, which can be understood as the motion of a body traversing a circular path at a constant speed. The angle between the acceleration and velocity in uniform circular motion is 90 degrees, as acceleration is directed towards the center of the circle (centripetal acceleration) while velocity is tangent to the circle at any instant. The body experiences centripetal acceleration due to the centripetal force. Angular acceleration is evaluated when the rate of change of angular velocity occurs over time.
For example, to calculate the centripetal force exerted on a 1,600 kg car rounding a 100 m radius curve at 12 m/s, we use the formula: F = mv²/r, where F is the centripetal force, m is the mass, v is the velocity, and r is the radius of the circular path. Substituting the given values, F = (1600 kg)(12 m/s)² / (100 m) which results in F = 2304 N.
Likewise, determining angular acceleration involves using the formula: \(\alpha = \frac{\Delta \omega}{\Delta t}\), where \(\alpha\) is the angular acceleration, \(\Delta \omega\) is the change in angular velocity, and \(\Delta t\) is the change in time. For instance, a gyroscope accelerating from rest to 32 rad/s in 0.40 s would have an angular acceleration \(\alpha = \frac{32 rad/s}{0.40 s} = 80 rad/s^2\). Understanding the connection between linear and angular acceleration helps in analyzing the movement of objects on a circular path.