Uniform Circular Motion Radians!

Force of Gravity

Gravitational Field Find gravitational field on the following: Find the mass of a 65-kg person on each

Change of Gravitational Field Find gravitational field on around Earth at: R = 2 radii of the planet R = 4 radii of the planet

Angular displacement

Angular displacement

1 radian in degrees

Which particle has angular position of

Rpm to rad/s If it takes 5 seconds to complete 10 rotations, find: Period of rotation T in seconds Frequency f of rotation Angular speed in rad/s How are T and f related? Angular displacement at 2.0 s Convert e) to degrees

Kinematics of the roulette wheel A small steel ball rolls counterclockwise around the inside of a 30.0 cm diameter roulette wheel. The ball completes exactly 2 rev in 1.20 s. What is the ball’s angular velocity? (Answer: 10.5 rad/s) What is the ball’s angular position at t = 2.00 s? Assume θi = 0. Express the answer in rad and degrees. (Answer: 2.1 rad, 120)

RPM in a car engine When your motor is running at 3000 rmp, what is the crankshaft’s angular velocity? (Answer: 314 rad/s)

Draw a displacement graph

Interpret the graph and draw Find angular speed of the wheel of the bike at t = 20 s, t = 50 s, t = 100 s, t = 160 s

Interpret the graph and draw

Angular and linear Derive the formula for v for an object that is moving around a circle.

Two points on a CD CD diameter is 12.0 cm. The maximum spinning rate is 540 rpm. What is the speed of a point a) 3.0 cm from the center, b) 6.0 cm from the center? Find angular and linear speeds for both. Which horse would you rather sit on on a merry-go-round? Why?

Acceleration in a UCM Draw a circle. Choose two points and draw the velocity vector at those points. Find the vector of the velocity change. What is the direction of the vector? If you divide that vector by a scalar representing the time it took the particle to move between those two points, what will you get? Explain the term ‘centripetal’ that is used for this acceleration.

Deriving ac

Compare For Emma and Jacob, compare: angular speed, tangential speed, angular acceleration, centripetal acceleration, period of rotation

Quasar Carnival Ride For safe operation, the maximum sustained acceleration is about 3g. Find the period of the ride at the maximum acceleration? (Answer 3.1 s)

Critical thinking

What is the source of ac?

Centripetal vs. centrifugal There is no centrifugal ‘force’ on the rider. What is his body doing?

Explain the physics of the spin cycle in a washing machine Washing machines Where do the socks go??? Explain the physics of the spin cycle in a washing machine

Various forces acting as Fc Two satellites orbit the Earth on the same orbit. Which would have to move faster: a heavier one or a lighter one? Prove your point mathematically by deriving the formula for orbital speed of a satellite.

Keppler’s III law Prove, using Newton’s ULG, assume orbits to be circular.

“Tarzan” problem A 65-kg person swings off a bank that is 6.0 m above the water on a tight 5.0 m rope. Find the force of tension in the rope at the bottom on the ark.

“Rollercoaster” problem A 45-kg skate boarder executes trick shown in the picture. The radius of the semi-circle is 3.0 m and the height to which the boarder rises h = 1.5 m. What is the normal force that the ramp is exerting on the boarder at the bottom of the ramp.

Force of friction as Fc - unbanked Calculate the maximum speed a 1500-kg car can have to safely execute a turn on a 75-m turn if the coefficient of static friction between the tires is 0.70. What speed can a car of similar make have if its mass is 3500 kg? What should the speed be on an icy road if the coefficient drops to 0.10?

Banked curves In terms of UCM, explain the purpose of banked turns of race-car courses. Draw an FBD and determine which force(s) act as centripetal in this case. Derive a formula for Fc in this case. Derive a formula for the angle on the banked curve if friction is neglected.

Force of tension A ‘swing’ ride at a carnival consist of chairs what a swung in a circle by 15.0-m cables attached to a vertical pole, as the drawing shows. Supposed the total mass of chair and its occupant is 179 kg. a) Determine the force of tension in the cable. b) Find the speed of the chair.