# Linear and Angular Velcity

1.

A large gear of diameter 30 cm is revolving at 45 rpm. It drives a small gear of diameter

8 cm.

a) How many radians per minute is the large gear tuning?

b) What is the linear velocity of the teeth on the large gear?

c) What is the linear velocity of the teeth on the small gear?

d) How many radians per minute is the small gear turning?

e) How many revolutions per minute is the small gear turning?

2.

Della Casee is riding a racing bike at a speed of 50.4 km/h. The wheels have a diameter

of 70 cm. Find the angular velocity of the wheels in radians per second.

3.

Dan Druff and Ella Funt are riding on a Ferris wheel. Dan observes that it takes 20

seconds to make a complete revolution. Their seat is 25 feet from the axle of the wheel.

a) What is their angular velocity in revolutions per minute?

b) ... in degrees per minute?

c) ... in radians per minute?

d) What is their linear velocity?

Thanks.

### 1 個解答

• 最佳解答

1.

a) How many radians per minute is the large gear tuning?

幫我看看吧

一圓周等於 360°， 單位是角度， degree。

b) What is the linear velocity of the teeth on the large gear?

幫我看看吧

circumferential of diameter 30cm = 2π x 30cm = 60π cm

The teeth travel 60π cm per revolution.

45rpm = 45 revolutions per minute = 45 x 60π cm per minute = 270π cm/minute

linear velocity = 270π cm/minute

c) What is the linear velocity of the teeth on the small gear?

幫我看看吧

It is the same as the larger one,

d) How many radians per minute is the small gear turning?

幫我看看吧

(30/8) x 45rpm x 2π rad/revolution = or = (30/8) x 90π rad/minute

e) How many revolutions per minute is the small gear turning?

幫我看看吧

2.

幫我看看吧

1 circumferential length of bike wheel = 70cm x π = 70π cm

(50.4km/h) / (70π cm/revolution) =72000/π revolution/h

72000/π revolution/h = 20/π revolution/sec

3.

a) What is their angular velocity in revolutions per minute?

幫我看看吧

radius = 25ft, diameter = 50ft

1 revolution takes 20 sec,

(60sec/minute) / (20sec/revollution) = 3 rpm

velocity = 3rpm

b) ... in degrees per minute?

幫我看看吧

3 rpm = 3 x 360 degree/minute = 1080 degree/minute

c) ... in radians per minute?

幫我看看吧

d) What is their linear velocity?

幫我看看吧幫我看看吧

circumferential = 25ft x 2 x π = 50 π ft

time taken for this circumferential = 20sec

Linear velocity = 50 π ft / 20 sec = 2.5 π ft / sec

幫我解釋一下

Linear Velocity 和 Angular Velocity

老師說：齊步走！

於是你就往前走，一秒鐘走一公尺，或兩秒鐘走一公尺，或三秒鐘走一公尺，快慢隨便你，1m/sec、1m/2sec、 1m/3sec、0.5m/sec、0.333m/sec 這些都是 Linear Velocity。

老師說：向右轉！

於是你就原地向右轉 90度角，一秒鐘就轉過來，或兩秒鐘才轉過來，或三秒鐘才轉過來，快慢隨便你，90°/sec、90°/2sec、 90°/3sec、45°/sec、30°/sec 這些就是 Angular Velocity。

2010-10-23 06:14:39 補充：

請問為何不滿意?????