<< Chapter < Page Chapter >> Page >

In figure a, a disk hitting a stick is compared to a tennis ball being hit by a racquet. When the ball strikes the racquet near the end with a force denoted by f ball as shown by the direction of the arrow, a backward force, f hand is exerted on the hand, In figure b, when the racquet is struck much farther down by a force F ball, a forward force, f hand is exerted on the hand as shown by the arrows. In figure (c), when the racquet is struck by the ball with a force f ball at the percussion point, no force is delivered to the hand. This implies that f hand is equal to zero.
A disk hitting a stick is compared to a tennis ball being hit by a racquet. (a) When the ball strikes the racquet near the end, a backward force is exerted on the hand. (b) When the racquet is struck much farther down, a forward force is exerted on the hand. (c) When the racquet is struck at the percussion point, no force is delivered to the hand.

Is rotational kinetic energy a vector? Justify your answer.

No, energy is always scalar whether motion is involved or not. No form of energy has a direction in space and you can see that rotational kinetic energy does not depend on the direction of motion just as linear kinetic energy is independent of the direction of motion.

Got questions? Get instant answers now!

Section summary

  • Angular momentum L is analogous to linear momentum and is given by L = size 12{L=Iω} {} .
  • Angular momentum is changed by torque, following the relationship net τ = Δ L Δ t .
  • Angular momentum is conserved if the net torque is zero L = constant net τ = 0 or L = L net τ = 0 . This equation is known as the law of conservation of angular momentum, which may be conserved in collisions.

Conceptual questions

Describe two different collisions—one in which angular momentum is conserved, and the other in which it is not. Which condition determines whether or not angular momentum is conserved in a collision?

Got questions? Get instant answers now!

Suppose an ice hockey puck strikes a hockey stick that lies flat on the ice and is free to move in any direction. Which quantities are likely to be conserved: angular momentum, linear momentum, or kinetic energy (assuming the puck and stick are very resilient)?

Got questions? Get instant answers now!

While driving his motorcycle at highway speed, a physics student notices that pulling back lightly on the right handlebar tips the cycle to the left and produces a left turn. Explain why this happens.

Got questions? Get instant answers now!

Problems&Exercises

Repeat [link] in which the disk strikes and adheres to the stick 0.100 m from the nail.

(a) 0.156 rad/s

(b) 1 . 17 × 10 2 J size 12{1 "." "17" times "10" rSup { size 8{ - 2} } " J"} {}

(c) 0 . 188 kg m/s size 12{0 "." "188 kg" cdot "m/s"} {}

Got questions? Get instant answers now!

Repeat [link] in which the disk originally spins clockwise at 1000 rpm and has a radius of 1.50 cm.

Got questions? Get instant answers now!

Twin skaters approach one another as shown in [link] and lock hands. (a) Calculate their final angular velocity, given each had an initial speed of 2.50 m/s relative to the ice. Each has a mass of 70.0 kg, and each has a center of mass located 0.800 m from their locked hands. You may approximate their moments of inertia to be that of point masses at this radius. (b) Compare the initial kinetic energy and final kinetic energy.

Figure a shows two skaters from the top view approaching each other from opposite directions with velocity v. In figure b two skaters then lock their right hands and start to spin in the clockwise direction with angular velocity omega.
Twin skaters approach each other with identical speeds. Then, the skaters lock hands and spin.

(a) 3.13 rad/s

(b) Initial KE = 438 J, final KE = 438 J

Got questions? Get instant answers now!

Suppose a 0.250-kg ball is thrown at 15.0 m/s to a motionless person standing on ice who catches it with an outstretched arm as shown in [link] .

(a) Calculate the final linear velocity of the person, given his mass is 70.0 kg.

(b) What is his angular velocity if each arm is 5.00 kg? You may treat the ball as a point mass and treat the person's arms as uniform rods (each has a length of 0.900 m) and the rest of his body as a uniform cylinder of radius 0.180 m. Neglect the effect of the ball on his center of mass so that his center of mass remains in his geometrical center.

(c) Compare the initial and final total kinetic energies.

Figure a shows a skater through an overhead view with both his hands outstretched. A ball is seen approaching toward him in air with velocity v. Figure b shows that skater catching two balls in his left hand, and then, recoiling toward the left, in clockwise direction, with angular velocity omega and finally, the balls have velocity v prime.
The figure shows the overhead view of a person standing motionless on ice about to catch a ball. Both arms are outstretched. After catching the ball, the skater recoils and rotates.
Got questions? Get instant answers now!

Repeat [link] in which the stick is free to have translational motion as well as rotational motion.

(a) 1.70 rad/s

(b) Initial KE = 22.5 J, final KE = 2.04 J

(c) 1 . 50 kg m/s size 12{1 "." "50 kg" cdot "m/s"} {}

Got questions? Get instant answers now!

Questions & Answers

What is specific heat capacity?
hamidat Reply
Specific heat capacity is the amount of heat required to raise the temperature of one (Kg) of a substance through one Kelvin
Paluutar
formula for measuring Joules
Rowshan Reply
I don't understand, do you mean the S.I unit of work and energy?
hamidat
what are the effects of electric current
ADAMS Reply
What limits the Magnification of an optical instrument?
Naeem Reply
Lithography is 2 micron
Venkateshwarlu
what is expression for energy possessed by water ripple
Prabesh Reply
what is hydrolic press
Mark Reply
An hydraulic press is a type of machine that is operated by different pressure of water on pistons.
hamidat
what is dimensional unite of mah
Patrock Reply
i want jamb related question on this asap🙏
sharon Reply
What is Boyles law
Pascal Reply
it can simple defined as constant temperature
Muhammad
Boyles law states that the volume of a fixed amount of a gas is inversely proportional to the pressure acting on in provided that the temperature is constant.that is V=k(1/p) or V=k/p
FADILAT
what is motion
Mua Reply
getting notifications for a dictionary word, smh
Anderson
what is escape velocity
Shuaibu Reply
the minimum thrust that an object must have in oder yo escape the gravitational pull
Joshua
what is a dimer
Mua
what is a atom
ADAMS
how to calculate tension
Deena Reply
what are the laws of motion
Mua
what is force
Ugwu Reply
Force is any quantity or a change that produces motion on an object body.
albert
A force is a push or a pull that has the tendency of changing a body's uniform state of rest or uniform state of motion in a straight line.
nicholas
plsoo give me the gravitational motion formulas
Okoye
f=Gm/d²
FADILAT
What is the meaning of emf
Chinedu Reply
electro magnetic force
shafiu
Electromotive force (emf) is a measurement of the energy that causes current to flow through a circuit.
Darssini
tritium (gas, netrogen, cloud, lamp)
firdaus Reply
Continue - > tritium (gas, netrogen, cloud, lamp span, lamp light, cool)
firdaus

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask