Acceleration in Nonuniform Circular Motion

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What is the formula for calculating the magnitude of the resultant acceleration in nonuniform circular motion?

$a = \sqrt{a_r + a_t}$

$a = a_r + a_t$

$a = a_r^2 + a_t$

$a = \sqrt{a_r^2 + a_t^2}$ (correct)

In which type of circular motion is only tangential acceleration present?

Radial circular motion

Linear motion

Uniform circular motion

Nonuniform circular motion (correct)

What is the relationship between the two acceleration vectors, ar and at, in nonuniform circular motion?

They are antiparallel to each other

They are both in the radial direction

They are perpendicular to each other (correct)

They are collinear

What is the direction of the resultant acceleration in nonuniform circular motion with respect to ac and ar?

At an angle between ac and ar Signup and view all the answers

What is the vector sum of centripetal and tangential acceleration in nonuniform circular motion?

$a = a_r + a_t$ Signup and view all the answers

What is the vector that represents the change in velocity in figure 1.3 (b)?

Av Signup and view all the answers

What is the geometric relationship between the triangle CAB in figure 1.3 (a) and the vector triangle in figure 1.3 (b)?

They are similar triangles Signup and view all the answers

What does a represent in the equation a = 2-1 = At Δυ Δε?

Time interval Signup and view all the answers

In figure 1.3 (c), what happens to As and Ae when At approaches zero?

As and Ae become zero Signup and view all the answers

What does centripetal acceleration point towards?

Perpendicular to the circle's radius Signup and view all the answers

Why is the acceleration directed towards the center of the circle called centripetal acceleration?

Because it points towards the center of the circle Signup and view all the answers

What can be said about the relationship between linear velocity and angular velocity in uniform circular motion?

They are equal at all times. Signup and view all the answers

In nonuniform circular motion, what does the negative angular acceleration signify?

The object is slowing down. Signup and view all the answers

How does the centripetal acceleration vector point in uniform circular motion?

Perpendicular to the linear velocity vector. Signup and view all the answers

What happens to the magnitude of velocity in nonuniform circular motion?

It varies randomly. Signup and view all the answers

How is centripetal acceleration related to the radius of curvature (r) in circular motion?

Directly proportional to r. Signup and view all the answers

What does it mean if the linear velocity vector is tangential to the path in circular motion?

The object is moving in a straight line. Signup and view all the answers

What is the analog of the linear motion equation v = vo + at in angular motion?

w = wo + at Signup and view all the answers

If the initial angular speed is wo and constant angular acceleration is a, what is the correct expression for the final angular speed w at time t?

w = wo + αt Signup and view all the answers

What is the relationship between linear motion's equation F = ma and angular motion's equation w² = w² + 2αθ?

F = Iω Signup and view all the answers

In the context of angular motion, what does the term 'θ' represent in the equation w² = w² + 2αθ?

Angular displacement Signup and view all the answers

If the equation derived is 0 = wt == W+ w two, what is the correct interpretation of the content?

Final angular speed equals initial angular speed plus angular displacement Signup and view all the answers

What analogy can be drawn between linear motion's equation s = v₁t+at² and angular motion's equation 0 = wot + - a t²?

(Time) squared times (angular velocity) equals (initial angular speed) minus (acceleration) times (time) squared Signup and view all the answers