Chapter 7.3Circular Motion

Uniform Circular Motion•Motion at constant speed in a circle

r1r1 r2 r2

v1

v2

v1

v2

r

v

r v r v

=

r v rt vt

=

v a r v

=

r/t = v v/t = a

ac = v2

r

Centripetal Acceleration (ac)

•Acceleration towards the center of a circle in uniform circular motion

ac = 42r

T2

Centripetal Force (Fc)

•The force that causes centripetal acceleration

Fc = mv2

r

Fc = m42r T2

A 5.0 kg ball is attached to the end of a 2.0 m string and swung at 4

revolutions per second. Calculate: ac & Fc

Drill: A 25 g ball is attached to the end of a

500.0 cm string and swung at 5.0 revolutions

per second.Calculate: ac & Fc

The NASA space station spins with a diameter of 100.0 m. Calculate the

period required to create an ac of 9.8 m/s2:

Calculate the speed a roller coaster must achieve to spin in a vertical circle with a diameter of 10.0 m:

A 2.5 kg ball is attached to the end of a 125 cm string and swung at 2.0 revolutions per second. Calculate: ac, vball, & Fc

A 50.0 kg box slides down an 250 m inclined plane

that is 37o from horizontal with an acceleration of 2.5 m/s2. Calculate F||, F, Fnet, Ff, vf, & on the incline and a & dH on the flat.

An arrow is fired at 50.0 m/s at 53o from

horizontal. Calculate:dH & dV at 1.0 s, 2.0 s, 3.0 s, & max dH & dV

A 10.0 g box slides down an 25 cm inclined plane ( = 0.20) that is

45o from horizontal. Calculate F||, F, FN, Ff,

Fnet, a, & vf on the incline.

Test Review

A ball thrown at 15 m/s from a 490 m tower.

Calculate: vV, dV & dH at 1.0 s, 2.0 s, 3.0 s, & maximum vV & dH

Drill: A bullet is fired horizontally at 750 m/s from a height of 4.9 m.

Calculate:tair, dH, & maximum vV

A ball is thrown from the ground at 20.0 m/s at an

angle of 53o from horizontal. Calculate:

tup, dVup, tair, & dH

A 40.0 g ball is traveling in a circular path with a diameter

of 10.0 cm at 25 cm/s. Calculate: ac & Fc

A 2500 kg carosel with a diameter of 20.0 m

spins at 6.0 revolutions per minute. Calculate:

ac & Fc