Rotational Motion Review Lesson

Rotational Motion Review Lesson

by Kurt Trout

​Unit Circle

• ​1 rev = 2π radians

• ​When calculating angular velocity, or how far a point moves around the circle...

• ​1 rev = 2 π radians. But velocity needs TIME! Always measure in rad/second

• ​So convert Rev per minute to Rad/Se

• ​1 Rev/min x 1 min/60 sec x 2π rad/sec

• ​

Multiple Choice

Convert 4 rpm to ang velocity? (Rad per second)

• 25 rad/s

• 0.42 rad/s

• 0.20 rad/s

​Some key equations!!

• for displacment (distance)

• ​X=r ø. (distance = radius x change)

• ​for velocity

• ​v=r w (linear velocity = radius x ang velocity)

• ​Linear Acceleration

• ​a=r∂. accel = radius x ang accel

• ​Agular accel

• ​∂ = w_f - w_i/t

Multiple Choice

The second hand on a watch is 12 mm long. What is the velocity of its tip?

• 0.0012 m/s

• 0.075 m/s

• 1.4 m/s

• 0/150 m/s

​So we want velocity...

​v = r w

​velocity = radius x ang velocity

​radius = 0.012 (remember, meters)

​ang velocity is 1 rev per minute, OR 2π/60 = 0.104 rad/s

​So v = (0.012)(0.104)= 0.0012 m/s

Multiple Choice

  

If a truck has a linear acceleration of 1.85 m/s² and the wheels have an angular acceleration of 5.23 rad/s², what is the diameter of the truck’s wheels?

• 0.707 m

• 0.354 m

• 2.82 m

• 5.65 m

Multiple Choice

In the spin cycle of a clothes washer, the drum turns at 635 rev/min. If the lid of the washer is opened, the motor is turned off. If the drum requires 8.0 s to slow to a stop, what is the angular acceleration of the drum?

• 8.3 rad/s

• 66.5 rad/s

• 79 rad/s

• 16.6 rad/s

Multiple Choice

A CD-ROM has a spiral track that starts 2.7 cm from the center of the disk and ends 5.5 cm from the center. The disk drive must turn the disk so that the linear velocity of the track is a constant 1.4 m/s. Find the following.

  the angular velocity of the disk (in rad/s and rev/min) for the start of the track

• 0.51 rad/s

• 52 rad/s

• 25 rad/s

• 17 rad/s

Multiple Choice

The outer edge of a truck tire that has a radius of 45 cm has a velocity of 23 m/s. What is the angular velocity of the tire in rad/s?

• 51 rad/s

• 10 rad/s

• 0.51 rad/s

• 8.3 rad/s