Does the angular displacement obey the commutative rule of vector addition.

Question

A car speeds up uniformly while rounding a turn of radius 13 meters. The car's angular speed increases from 0.52 radians per second to 0.98 radians per second as it turns through 1.30 radians. a. At the instant the angular speed is 0.76 radians per second, what is the car's centripetal acceleration? Include units in your answer. b. At the instant the angular speed is 0.76 radians per second, what is the car's tangential acceleration? Include units in your answer

Answer 1

Question

Definition Definition Angle at which a point rotates around a specific axis or center in a given direction. Angular displacement is a vector quantity and has both magnitude and direction. The angle built by an object from its rest point to endpoint created by rotational motion is known as angular displacement. Angular displacement is denoted by θ, and the S.I. unit of angular displacement is radian or rad.

Chapter 12, Problem 10PQ

To determine

Does the angular displacement obey the commutative rule of vector addition.

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A car speeds up uniformly while rounding a turn of radius 13 meters. The car's angular speed increases from 0.52 radians per second to 0.98 radians per second as it turns through 1.30 radians. a. At the instant the angular speed is 0.76 radians per second, what is the car's centripetal acceleration? Include units in your answer. b. At the instant the angular speed is 0.76 radians per second, what is the car's tangential acceleration? Include units in your answer

A figure skater is spinning with her arms outstretched. She completed 4 full revolutions in 2 seconds. a) her fingertip travels in a circle of radius 80cm. How far does her fingertip travel in the 2 seconds? b) what is the linear velocity of her fingertip in centimeters per second? c) the end of her shoulder is 18cm from her axis of rotation. What would be the difference in her angular velocity and linear velocity, if any, and explain why?

A cyclist is travelling in a straight path at a constant speed along a dirt road with a button stuck to the outside of one of their wheels. The movement of the button (as viewed from the side) can be described using the equations of a cycloid, x = r(t − sin t), y = r(1 − cost) where t represents the angle through which the wheel has rotated and r represents the radius of the wheel. a) Every time the button touches the ground, it leaves a mark on the dirt. If the marks are 64π cm apart, what is the radius of the tire wheel? (b) What value(s) of t correspond to the button touching the ground? (c) Show that when t = 2π, we have dx/dt = 0. Does this mean that the cyclist is stopped? Why or why not?

Answer 2

Question

Definition Definition Angle at which a point rotates around a specific axis or center in a given direction. Angular displacement is a vector quantity and has both magnitude and direction. The angle built by an object from its rest point to endpoint created by rotational motion is known as angular displacement. Angular displacement is denoted by θ, and the S.I. unit of angular displacement is radian or rad.

Chapter 12, Problem 10PQ

To determine

Does the angular displacement obey the commutative rule of vector addition.

Expert Solution & Answer

Trending nowThis is a popular solution!

See solution

Check out sample textbook solution

Answer 3

Question

Definition Definition Angle at which a point rotates around a specific axis or center in a given direction. Angular displacement is a vector quantity and has both magnitude and direction. The angle built by an object from its rest point to endpoint created by rotational motion is known as angular displacement. Angular displacement is denoted by θ, and the S.I. unit of angular displacement is radian or rad.

Chapter 12, Problem 10PQ

To determine

Does the angular displacement obey the commutative rule of vector addition.

Expert Solution & Answer

Trending nowThis is a popular solution!

See solution

Check out sample textbook solution

Answer 4

Question

Definition Definition Angle at which a point rotates around a specific axis or center in a given direction. Angular displacement is a vector quantity and has both magnitude and direction. The angle built by an object from its rest point to endpoint created by rotational motion is known as angular displacement. Angular displacement is denoted by θ, and the S.I. unit of angular displacement is radian or rad.

Chapter 12, Problem 10PQ

To determine