Concept #1: Rotational Velocity & Acceleration

Example #1: Rotational velocity of Earth

Practice: Calculate the rotational velocity (in rad/s) of a clock’s minute hand.

EXTRA: Calculate the rotational velocity (in rad/s) of a clock’s hour hand.

Practice: A wheel of radius 5 m accelerates from 60 RPM to 180 RPM in 2 s. Calculate its angular acceleration.

As a particle with a velocity v in the negative x direction passes through the point (0, 0, 1), it has an angular velocity relative to the origin that is best represented by vector
A. 1
B. 2
C. 3
D. 4
E. Zero

A wheel of radius 0.5 m rolls without slipping on a horizontal surface. Starting from rest, the wheel moves with a constant angular acceleration of 6 rad/s2 . The distance traveled by the center of the wheel from t = 0 to t = 3 s is about:
A. none of these
B. 2.1 m
C. 13.5 m
D. 18 m
E. 27 m

When you look up into the sky, you always see the same part of the moon, no matter what time of the month or year it is. In order to achieve this, the rotational period of the moon must be equal to its orbital period (how long it takes to orbit the Earth). Given this fact, what is the angular velocity of the moon due to its spinning about its own axis?

When you ride your bicycle, in what direction is the angular velocity of the wheels?
A) to your left
B) to your right
C) forward
D) backward
E) up

Two solid discs are rotating about a perpendicular shaft through their centers, as shown in the figure. Disc A, has a radius that is twice as large as disc B,? Which of the following statements is NOT true?
A) A point on the rim of disc A, has twice the linear speed as a point on the rim of disc B.
B) The direction of the angular velocity is to the right.
C) Every point on the body has the same angular acceleration.
D) The linear acceleration of a point on the rim of disc B is the same as the linear acceleration of a point halfway from the center to the rim on disc A.
E) The angular velocity at a point on the rim of disc A is twice the angular velocity of a point on the rim of disc B.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential speed?A) Child BB) They have the same zero tangential speedC) Child AD) They have the same non-zero tangential speedE) There is not enough information given to answer the question.