University Physics Al No 8 Spin and Orbital Motion Class Number ame L. Choose the Correct Answer A particle moves with position given by P= 3ti +4j, where F is measured in meters when t is measured in seconds. For each of the following, consider only 1>0. The magnitude of the angular momentum of this particle about the origin is (A)increasing in time. (B)constant in time. (C)decreasing in time. (D)undefined Solution: Assume the mass of the particle is m, so the angular momentum of this particle about the L=F×P=Fxm=Pmx,=(3n+4)×m(31)=-12mk Thus the magnitude of the angular momentum of this particle L=12mkg m /s=constant 2. A particle moves with constant momentum p=(10kg. m/s)i. The particle has an angul momentum about the origin of L=(20kg. m/s)k when [=Os. The magnitude of the angul momentum of this particle is (A)decreasing (B) not necessarily constant Solution: The angular momentum of this particle about the origin is L=rx P, so the position vector of the particle when (=Os is r=-2j Assume the mass of the particle is m, the position vector of the particle at any time t is F=vti-2j=Pni-2 So the angular momentum of this particle L=fxP=(Pti-2j) Pi=2pk=20kg. m/s)k Thus the magnitude of the angular momentum of this particle L=20kg. m"/s=constant 3. A solid object is rotating freely without experiencing any external torques. In this case (a A)Both the angular momentum and angular velocity have constant direction (B)The direction of angular momentum is constant but the direction of the angular velocity might not be constant (C)The direction of angular velocity is constant but the direction of the angular momentum mightUniversity Physics AI No. 8 Spin and Orbital Motion Class Number Name I. Choose the Correct Answer 1. A particle moves with position given by r ti j = 3 ˆ + 4 ˆ v , where r v is measured in meters when t is measured in seconds. For each of the following, consider only t > 0. The magnitude of the angular momentum of this particle about the origin is （ B ） (A) increasing in time. (B) constant in time. (C) decreasing in time. (D) undefined Solution: Assume the mass of the particle is m, so the angular momentum of this particle about the origin is ti j m i mk t r L r P r mv r m ˆ (3 ˆ 4 ˆ) (3ˆ) 12 d d = × = × = × = + × = − v v v v v v r Thus the magnitude of the angular momentum of this particle 12 kg m /s constant 2 L = m ⋅ = . 2. A particle moves with constant momentum p i ˆ = (10kg ⋅m/s) r . The particle has an angular momentum about the origin of L k ˆ (20kg m /s) 2 = ⋅ r when t = 0s. The magnitude of the angular momentum of this particle is （ B ） (A) decreasing (B) constant. (C) increasing. (D) possibly but not necessarily constant. Solution: The angular momentum of this particle about the origin is L r P v v r = × , so the position vector of the particle when t = 0s is r j = −2 ˆ v . Assume the mass of the particle is m, the position vector of the particle at any time t is ti j m p r vti j = ˆ − 2 ˆ = ˆ − 2 ˆ v So the angular momentum of this particle is ti j Pi pk k m p L r P ˆ (20kg m /s) ˆ ( ˆ 2 ˆ) ˆ 2 2 = × = − × = = ⋅ v v r Thus the magnitude of the angular momentum of this particle 20kg m /s constant 2 L = ⋅ = . 3. A solid object is rotating freely without experiencing any external torques. In this case （ A ） (A) Both the angular momentum and angular velocity have constant direction. (B) The direction of angular momentum is constant but the direction of the angular velocity might not be constant. (C) The direction of angular velocity is constant but the direction of the angular momentum might